Mr.DeMeo - HOMEWORK

7ACC
Unit 11
2-D Figures
| |Date |Lesson |Topic |
| | |1 |Area of Triangles & Quadrilaterals |
| | |2 |Similar Figures with Perimeter and Area |
| | |3 |Finding Area of Circles |
| | |4 |Finding Circumference of Circles |
| | |5 |Area vs. Circumference |
| | | |Review |
| | | |Test |
| | | | |
Lesson 1
Area of Triangles & Quadrilaterals
Types of Triangles:
|Name of Triangle |Definition/Picture |Name of Triangle |Definition/Picture |
|Acute Triangle | |Scalene Triangle | |
|Right Triangle | |Isosceles Triangle | |
|Obtuse Triangle | | Equilateral | |
| | |Triangle | |
The sum of the measures of the angles of any triangle is ________________________
Classifying Quadrilaterals
A parallelogram is ________________________________________
________________________________________________________
________________________________________________________
A rectangle is ____________________________________________
________________________________________________________
A rhombus is ____________________________________________
________________________________________________________
A square is _______________________________________________
_________________________________________________________
A trapezoid is ___________________________________________
________________________________________________________
The sum of the measures of the angles of any quadrilateral is ________________________
Area Formulas of Triangles and Quadrilaterals
Definitions:
Area is _____________________________________
Altitude is __________________________________
• An altitude is needed when a figure doesn’t have a side with a 90[pic] angle.
A composite figure is made up of two or more shapes.
To find the area of a composite figure, decompose the figure into shapes with areas you know. Then find the sum of these areas.
~ When finding the Area of a figure always Square your units. ~
Shape Picture Area Formula
Find the Area of each figure:
1. 2.
3. 4.
5. 6.
7. Find the area of the following composite figures.
5m 5m Figure 1 Figure 2 Total
12m 2m
Find the missing dimension, given the area (solve algebraically):
8. The area of a square is 400 square units. What is the distance of each side?
9. The area of a rectangle is 240 square units. If the length of the rectangle is 24 units, what is the width?
10. The area of a parallelogram is 54 square feet. If the height of this figure is 9 feet, how
long is the base?
11. A trapezoid has an area of 240 square feet. The measures of the bases are 10 units and 16 units, respectively. What is the height of this trapezoid?
12. A triangular monument is being constructed in a park. The total area of the monument is 280 square units, and the base is 28 feet wide. How tall is the monument?
13. A rectangular room has an area of 600 square feet. The length of the room is 30 feet, what is the width?
14. What is the area of a triangle with a height of 24 feet and a base of 10 feet?
15. James is comparing the dimensions of a triangle and a rectangle. The two shapes have the same area. The height of the triangle is 20 feet, and the length of the rectangle is also 20. If the width of the rectangle is 40 feet, what must the base of the triangle be?
Lesson 1 – Homework
Find the Area of each figure:
1. 2.
3. 4.
5. 6.
7. Find the area of the composite figure
4cm Figure 1 Figure 2 Total
6cm
Find the missing dimension, given the area (solve algebraically):
8. The area of a square is 169 square units. What is the distance of each side?
1. The area of a rectangle is 120 square units. If the length of the rectangle is 5 units, what is the width?
Lesson 2
Similar Figures
Vocabulary
Congruent figures: Same shape, same size
Similar figures: Same shape, but NOT necessarily the same size
Corresponding: _____________________________________________________________________
For this reason, all congruent figures are similar, but not all similar figures are congruent.
Similar Figures have the following properties:
• Their corresponding sides have proportional lengths.
• Their corresponding angles are congruent.
Steps to finding the Perimeter or Area of Similar Figures:
• Always find the missing side first. (Set up a proportion to find missing side)
• Once all sides are present, use the correct formula to find perimeter/ area.
Examples
*Angles are congruent since all
5cm 2.5cm rectangles have four right angles.
7.5cm 3.75cm
The ratios of the lengths and widths of the rectangles are in proportion.
[pic] = [pic] (Cross multiply) *Therefore, the rectangles are similar because,
the rectangles have congruent angles and
18.75 = 18.75 corresponding sides are in proportion.
State whether the following are Similar Figures or Not.
1) 2) 8in
6m
1.5m 12in 16i n
4m 1m 3in
The following figures are similar. Find the missing side.
3) 4)
8m 4m 10cm 6cm x
5cm
10m x
Find the perimeter of each of the following similar figures.
5) 6)
14m 14m
7m 7m 1.5m x
10m x 2m 4m
Find the area of each of the following similar figures.
7) 8)
15m 2m 3cm 15cm
30m x 4cm x
Try These
1) A gate is 3 feet and casts a shadow 5 feet long. At the same time, a nearby building casts a shadow
45 feet long. What is the height of the building?
A. 15 feet B. 27 feet C. 43 feet D. 75 feet
2) Which describes these two figures?
A. Congruent but not similar
B. Neither similar nor congruent
4m 3m C. Similar but not congruent
D. Similar and congruent
6m 4.5m
3) The following right triangles are similar. Find the length for the side representing x.
A. 72 cm
B. 78 cm
C. 128 cm
96 cm 104cm x D. 139 cm
40cm 30cm
4) Justin has two rectangular photo prints that are similar. The length of the smaller print is 5 inches
and the width is 3 inches. The length of the larger print is 20 inches.
a) Find the width of the larger print.
b) Find the perimeter of the smaller print.
c) Find the Area of the larger print.
5) The ratio of the corresponding sides of two similar triangles is 4:9. The sides of the smaller
triangle are 10cm, 16cm, and 18cm.
a) Find the three dimensions of the larger triangle.
b) Find the perimeter of the larger triangle
Lesson 2 – Homework (2 pages)
Determine if the following polygons are similar or not similar:
1. 2.
12.5m
3.1m 8m 20m
7.5m 2m 3m 7.5m
Each pair of figures below is similar. Find the value of each variable.
3. 4. 12m n
30m 54m 6m 3m
45m y
5. A woman is 5 ft. tall and her shadow is 4 ft. long. A nearby tree has a shadow 30 ft. long. How tall
is the tree?
6. Paula casts a shadow 2 meters long at the same time a tree casts a shadow 28 meters long. The tree
is 17.5 meters tall. How tall is Paula?
7. ABC is similar to PQR. Find each measure.
C R 1) Length of AB
21 ft 14 ft 2) Length of RP
16.8 ft 3) Measure of [pic]A
53[pic] B 92[pic] Q 4) Measure of [pic]Q
A P 8 ft
8. An image is 16 in. by 20 in. You want to make a copy that is similar. Its longer side will be 38 in.
The copy costs $0.60 per square inch. Estimate the copy’s total cost.
9. You want to enlarge a copy of the flag of the Philippines that is 4 in. by 8 in. The two flags will be
similar. How long should you make the shorter side if the long side is 24 ft.?
Find the Perimeter of each figure. Find the Area of each figure
10. 11.
x 4cm
6m 9m
8m x 12.5cm 5cm
Review
12. 5x – 9 + 10 = 31 13. -2(4x + 9) = 30 14. 8x – 10x + 8 = -20
Simplify:
15. 4x + 2(3x + 4) 16. – 5(x – 8) – 12 17. (4x – 4)[pic] + 4x – 3
Factor:
18. 12x + 16 19. 15x + 30 20. 18x – 45
Lesson 3
Finding Area of a Circle
Shade the Area of the Circle Shade the Circumference of the Circle
Diameter – a line segment that passes through the center of the circle.
Radius – is a line segment that extends from the center of a circle to
any point on the circle.
To find the Area of a circle follow the following steps:
1) Write d =_____, r =_______
2) Write formula:
3) Substitute for r.
4) See how the answer should be shown. (Rounding or in terms of π)
Examples
a) r = 5 d = ______ b) r = 9 d = _______ c) r = ______ d = 8
d) r = _____ d = 12 e) r = 50 d = _______ f) r = 1 d = ______
g) r = 3 r2 = _____ h) r = 5 r2 = _______ i) r = 1 r2 = _____
Find the Area:
1)
Write r = ______
d = ______
Formula:
Substitute:
Solve: Answer in terms of π ________
Round answer to the nearest tenth _____
Find the area in terms of pi. Find the area and round to the nearest tenth.
2) r = ____ d = _____ 4) r = ____ d = _____
Write formula
3) r = ____ d = _____ 5) r = ____ d = _____
Given the Area, find the radius and diameter.
6) A = 49[pic] 7) A = 81[pic] 8) A = 16[pic] 9) A = 25[pic]
r = ______ r = ______ r = ______ r = ______
d = ______ d = ______ d = ______ d = ______
10) What is the radius and diameter of a circle with an Area equal to 113.04 sq. m? ________________
Find the Area of the following semicircles. (Round to nearest Tenth.)
11) A = ______ 12) A = ________
Diameter is 20 m Radius is 8.2 ft
Try These:
Find the Area of the following circles in terms of pi and to the nearest tenths place.
1) r = ____ d = _____ 2) r = ____ d = ______
3) 4) r = ____ d = ____
r = ____ d = _____
Given the Area, find the radius and diameter.
5) A = 121[pic] 6) A = 9[pic] 7) A = 225[pic] 8) A = 4[pic]
r = ______ r = ______ r = ______ r = ______
d = ______ d = ______ d = ______ d = ______
9)The area of a circle is 154 sq. m. What is the radius? ________________
What is the diameter? ______________
Lesson 3 - Homework
Find the Area of the following circles. Round your answer to the nearest tenth.
1) r = ____ d = _____ 2) r = ___ d =_____
A = A =
3) r = _____ d = ______ 4) r = ____ d =______
A = A =
Given the Area, find the radius and diameter.
5) A = 16Ï€ 6) A = 144Ï€
7)How much icing is needed to cover a Cake that has a diameter of 16 inches? (Leave in terms of π)
8) Find the area of the following: (careful it is a half circle) 9) Find the area of the circle below:
Round your answer to the nearest foot. Leave answer in terms of pi.
[pic]
Lesson 4
Finding Circumference of a Circle
To find the Circumference of a circle follow the following steps:
1) Write r =_____ d =_______
2) Write formula:
3) Substitute for d.
4) See how the answer should be shown. (Rounding or terms of π)
Examples:
Finding the Circumference
1)
Write r = ______
d = ______
Formula:
Substitute:
Solve:
Answer in terms of π ________
Round answer to the nearest tenth________
Find the circumference: In terms of π.
2) r = ____ d = _____ 3) r = ____ d = _____
Round to the nearest tenth.
4) r = ____ d = _____ 5) r = ____ d = _____
Find the Circumference of the following semicircles. (Round to nearest Tenth.)
6) C = ______ 7) C = ________
Diameter is 20 m Radius is 8.2 ft
Given the circumference, find the radius and diameter:
8) C = 4[pic] 9) C = 20[pic] 10) C = 50[pic] 11) C = 100[pic]
r = ______ r = ______ r = ______ r = ______
d = ______ d = ______ d = ______ d = ______
12) C = 81.7m 13) C = 94.2m 14) C = 18.8 ft 15) C = 188.5 ft
r = ______ r = ______ r = ______ r = ______
d = ______ d = ______ d = ______ d = ______
Try These:
Find the Circumference of the following circles in terms of pi and to the nearest tenths place.
1) r = ____ d = _____ 2) r = ____ d = ______
3) 4) r = ____ d = ____
r = ____ d = _____
Given the circumference, find the radius and diameter:
5) C = 80[pic] 6) C = 25[pic] 7) C = 36[pic] 8) C = 62[pic]
r = ______ r = ______ r = ______ r = ______
d = ______ d = ______ d = ______ d = ______
9) C = 50.3m 10) 150.8 ft 11) C = 12.6m 12) C = 100.5 ft
r = ______ r = ______ r = ______ r = ______
d = ______ d = ______ d = ______ d = ______
13) Chef Pierre uses vegetables grown in his new circular garden. He knows that the area of his garden is 15 square meters. He wants to build a path through the middle of the circular garden. What will be the approximate length of the new path?
New path design
A) 1.2m B) 2.2m C) 4.4m D) 7.2m
Lesson 4 - Homework
Find the Circumference of the following circles. Round your answer to the nearest tenth.
1) r = ____ d = _____ 2) r = ___ d =_____
C = C =
3) r = _____ d = ______ 4) r = ____ d =______
C = C =
5) How much fencing is needed for a garden that has a diameter of 10 ft? (Round to nearest tenth)
7) Joan determined the area of the circle below to be 400 í µí½… cm2 but Melinda says the area is 100 í µí½… cm2.
Who is correct? Why?
[pic]
Review:
8) Find the missing angle 9) Find the area of these two similar rectangles
9m 6m
12m x
Lesson 5
Area vs. Circumference
Sometimes you will be given the Area and be asked to find the Circumference.
Remember:
Steps:
1) Using the Area formula, plug in the given Area for A
2) Find the Radius by solving for r
3) Find the Diameter and use the Circumference formula to find the Circumference.
Examples
Find the Circumference of each in terms of[pic].
1) A = 25[pic] 2) A = 4[pic] 3) A = 121[pic]
Find the Circumference. Round to the nearest hundredth.
4) A = 153.938 m[pic] 5) A = 254.469 cm[pic] 6) A = 28.2743 ft[pic]
Sometimes you will be given the Circumference and be asked to find the Area.
Remember:
Steps:
1) Using the Circumference formula, plug in the given Circumference for C
2) Find the Diameter by solving for d
3) Find the Radius and use the Area formula to find the Area.
Find the Area of each in terms of[pic].
7) C = 10[pic] 8) C = 44[pic] 9) C = 8[pic]
Find the Area. Round to the nearest hundredth.
10) C = 37.6991 m 11) C = 62.8318 cm 12) C = 43.9822 ft
Try These
1) Hardy’s Pizzeria is having a sale on medium and large pizzas. Medium pizzas are 10 inches in
diameter and cost $7.99. Large pizzas have an area of 254 in[pic] and cost $14.99. Which size pizza
is the better deal? Explain.
______________________________________________________________________________________________________________________________________________________________________
2) If the length of the radius of a circle is doubled, how does that affect the circumference and area?
Explain.
______________________________________________________________________________________________________________________________________________________________________
3) Every year in September, Sue covers her circular pool. Her pool has a diameter of 25 feet. Find
how much covering she will need.
4) At a local park, Sara can choose between two circular paths to walk. One path has a diameter of 120
yards, and the other has a radius of 45 yards. How much further can Sara walk on the longer path
than the shorter path if she walks the path once?
5) Lana is putting lace trim around the border of a circular tablecloth. The tablecloth has a diameter of
1.2 meters. To the nearest meter, what is the least amount of lace she needs?
A. 3m B. 4m C. 7m D. 8m
6) The circle below has a diameter of 12 cm. Calculate the area of the shaded region.
[pic]
Lesson 5 - Homework
1) Given: A = 36[pic] 2) Given: C = 30[pic]
Find the Circumference in terms of [pic] Find the Area in terms of [pic]
3) Given: A = 452.3893m[pic] 4) Given: C = 50.2654cm[pic]
Find the Circumference round to nearest tenth. Find the Area rounded to nearest tenth.
5) A circular swimming pool has a radius of 15 feet. The family that owns the pool wants to put up a
circular fence that is 5 feet away from the pool at all points.
a) Find the radius of the fenced in area.
b) Find the amount of fencing needed.
6) What is the radius of a circle when the circumference is 16[pic] cm?
7) A circular rose garden needs new sod. The diameter of the garden is 18 feet. How much sod is
needed to cover the rose garden?
8) The front wheel of a high-wheel bicycle from the late 1800s was larger than the rear wheel to
increase the bicycle’s overall speed. The front wheel measured in height up to 60 in. Find the
circumference and area of the front wheel of the high-wheel bicycle.
9) Use the [pic] key on the calculator to find the area of a circle whose radius is 5.6m. Which is the better
estimate? 98m[pic] or 99m[pic]? Explain.
______________________________________________________________________________________________________________________________________________________________________
Name: ___________________________________________ Date: _________________
7ACC Unit 11 2D Figures Review
1) What is the best name of this quadrilateral?
_________________ __________________ __________________
Find the Area
2) 3) 4)
6m 8m 5.5m
9m 11m 4.2m
5) 7cm 6) 10m
5cm 8m
9cm
Find the area of the irregular figure.
7) 8m
5m
2m
8) Which figure has the least area?
A. Square with a side length of 11 cm
B. Parallelogram with a base of 8cm and height of 11cm
C. Triangle with a base of 18cm and a height of 4cm
D. Rectangle with a width of 5cm and a length of 18cm
The following figures are similar. Find the missing side.
40in
9) 10) 11)
12m 6m 18cm 12cm 160in 30in
20m x 6cm x
x
12) A man is 5 ft. tall and his shadow is 3 ft. long. A nearby tree has a shadow 6 ft. long. How
tall is the tree?
13) Jenny casts a shadow 4 meters long at the same time a tree casts a shadow 26 meters long.
Jenny is 22 meters tall. How tall is tree?
Find the perimeter of the following similar figure. Find the area of the following similar figure.
14) 15)
20m 20m 15m 5m
10m 10m
30m x
5m x
16) Kelly has two rectangular photo prints that are similar. The length of the smaller
print is 4 inches and the width is 5 inches. The length of the larger print is 20 inches.
a) Find the width of the larger print.
b) Find the perimeter of the smaller print.
c) Find the area of the larger print.
Find the circumference and area in terms of pi.
17) C = ____ A = _____ 18) C = ____ A = _____
Find the circumference and area to the nearest tenth.
19) C = ____ A = _____ 20) . C = ____ A = _____
21) How much covering is needed to cover a Cake that has a diameter of 12 inches? (Leave in
terms of π)
Find the circumference of each in terms of [pic]. Find the circumference to the nearest hundredth.
22) A = 36[pic] 23) A = 9[pic] 24) A = 452.3893 m[pic] 25) A = 314.1592 cm[pic]
Find the area of each in terms of [pic]. Find the area rounded to the nearest hundredth.
26) C = 12[pic] 27) C = 8[pic] 28) C = 62.8318 m 29) C = 113.0973 cm
30) The window that is in the shape of a semicircle has a diameter of 12 inches. Find the area of
the window. Round to the nearest tenth.
31) Kara wants to put fencing around her pool. Her pool has a diameter of 14 feet. Find
how much fencing she will need.
32) What is the radius of a circle when the circumference is 25[pic] cm?
-----------------------
10
4
8
16
20
12
4
20
9
7
9
9
15
20
11
4
10
2.5
1.2
10
50
8
5
90
12
90
diameter
radius
[pic]
4m
24m
3m
10m
9m[pic]m
8m
3m
10m
50m
18m
8m 8888m
6m
22m
[pic]
12m
13m
7m
24m
4m[pic]m
8m
3m
5m
50m
10m
18m
8m 8888m
6m
22m
100[pic]
135[pic]
70[pic]
x
[pic]
[pic]
5m
12m
8m[pic]m
4.5m
................
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