9 Area, Perimeter and Volume MEP Y9 Practice Book B
[Pages:27]9 Area, Perimeter and Volume MEPY9PracticeBookB
9.1 2-D Shapes
The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes.
Rectangle Square
All angles are right angles ( 90 ?) Opposite sides have the same length
All the sides have the same length All angles are right angles (90 ?)
Parallelogram
Opposite sides have the same length
Rhombus
All the sides have the same length
Diagonals bisect at right angles
Trapezium
Kite Isosceles Triangle Equilateral Triangle
Diagonals intersect at right angles
Two sides have the same length and the angles opposite these two sides are equal
All angles are 60 ?
1
9.1
MEP Y9 Practice Book B
Example 1
Draw the lines of symmetry of an equilateral triangle.
Solution
There are 3 lines of symmetry, as shown in the diagram. They join each vertex (corner) to the midpoint of the opposite side.
Example 2
Name each of the following shapes:
(a)
15 cm
(b)
100 ?
15 cm
15 cm
40 ?
40 ?
15 cm
Solution
(a) This is a rhombus because all the sides have the same lengths. (b) This is an isosceles triangle because two of the angles are the same size.
Example 3
State the order of rotational symmetry of:
(a) a trapezium,
(b) a parallelogram.
Solution
(a) 1
(b) 2 (unless the parallelogram happens to be a square, in which case the order of rotational symmetry would be 4).
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MEP Y9 Practice Book B
Exercises
1. Name each of the following shapes:
(a)
6 cm
(b)
5 cm
4 cm
5 cm
5 cm
(c) 4 cm
(d) 6 cm
5 cm 80?
4 cm
6 cm
50?
50?
(e)
4 cm 60?
10 cm
(f)
4 cm 60?
60?
60?
60?
2. Draw diagrams to show the lines of symmetry of:
(a) a kite,
(b) a square,
(c) a rectangle,
(d) an isosceles triangle.
3. How many lines of symmetry are there for:
(a) a parallelogram,
(b) a rhombus ?
4. State whether each of the following statements is true or false. (a) A square is also a rhombus. (b) A square is also a kite. (c) A rectangle is also a kite. (d) A parallelogram is also a kite. (e) A rectangle is also a parallelogram.
5. Write down the order of rotational symmetry of:
(a) a rhombus,
(b) a square,
(c) an isosceles triangle, (d) an equilateral triangle,
(e) a kite.
3
9.1
MEP Y9 Practice Book B
6. A triangle has one line of symmetry. What type of triangle is it?
7. Draw a trapezium that has: (a) one line of symmetry,
(b) no lines of symmetry.
8. A right-angled triangle is also an isosceles triangle. What sizes are the other angles in this triangle?
9. For a semicircle: (a) draw a diagram to show its lines of symmetry, (b) state its order of rotational symmetry.
10. (a) Draw a diagram to show the lines of symmetry of a regular pentagon. (b) State the order of rotational symmetry of a regular octagon.
11. Rosemary drew these rectangles using a computer:
D
C B A
5
Rectangle A has width 3 and length 5: 3
The computer repeated these instructions to draw the other rectangles: new width = previous width ? 2 new length = previous length + previous width
Copy and complete this table. width
length
rectangle A
3
5
rectangle B
......
......
rectangle C
......
......
rectangle D
......
......
(KS3/94/Ma/3-5/P1)
4
MEP Y9 Practice Book B
9.2 Area of Special Shapes
In this section we calculate the area of various shapes.
Area of a circle
= r2
r
Area of a triangle
= 1bh 2
Area of a parallelogram = b h
h
b
(h is perpendicular height)
h b
Example 1
Calculate the area of the triangle shown.
Solution
Area = 1 ? 4 ? 6 2
4 cm
= 12 cm2
Example 2
Calculate the area of a circle with diameter 10 m.
Solution
Radius = 10 ? 2 = 5 m Area = ? 5 2 = 78.53981634 m2
= 78.5 m 2 (to 3 significant figures)
Example 3
Calculate the area of the shape shown:
6 cm 8 m
4 m
5
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