Mini-Project: Perimeter and Area of Triangles

Mini-Project: Perimeter and Area of Triangles

The perimeter, P, of a figure is the sum of the side lengths of the figure. Perimeter is a linear measure meaning it is measured in in, ft, mi, cm, m, and km, etc. To find the perimeter of a triangle, add the measures of the three sides of the triangle.

P = a + b + c where a, b, and c are the measures of the sides of the triangle.

The area, A, of a figure is the number of non-overlapping square units that exactly cover the figure. Area is a square measure meaning it is measured in in2, ft2, mi2, cm2, m2, and km2, etc.

To find the area of a triangle, multiply ? times the base times the height of the triangle.

A = ? bh where b is the length of the base and h is the length of the height of the triangle.

Note: the base and height of a triangle always form a right angle.

Open the book to page 36 and read example 1. Example: Find the perimeter and area of the triangle.

P = a + b + c = 6 + x + 4 + 5x = 6x + 10 P = 6x + 10

A = ? bh = ? (6)(x+ 4) = 3(x + 4) = 3x + 12 A = 3x + 12

5x x + 4

6

Practice: Find the perimeter and area of the triangle. (2 points)

P = ____________________

2x + 3

A = ____________________

Complete pgs. 38 ? 39 prob. 5, 12, 19, 20, 29, 33, 34. (12 points) 5. P = _________________ A = _________________ 12. P = _________________ A = _________________ 19. A = _________________ 20. h = _________________ 29. equation: ________________________________ b = _________________ h = _________________ 33. h = _________________ 34. b = _________________

8x - 5 10

The perimeter and area of a triangle can be determined if the triangle is described in terms of its coordinates on a graph. Example: Graph ABC with vertices A(-5, 2), B(-3, 5) and (2, 2). Determine its perimeter.

Recall: The distance between ordered pairs can be determined by using the distance formula.

d x 2 x1 2 y2 y1 2

B

AB = d - 3 52 5 22 4 9 13 3.6

BC = d 2 32 2 52 25 9 34 5.8 A

C

CD = d 2 52 2 22 49 0 7

P = 3.6 + 5.8 + 7 = 16.4

Practice: Graph DEF with vertices D(-5, -4), E(3, -1), F(3, -4). Determine its perimeter. (5 points) DE = _______________ EF = _______________ DF = _______________ P = _______________

Example: Determine the area of ABC.

Recall: Base and height must meet at a right angle

and on a graph horizontal and vertical segments

B

always meet at a right angle.

AC is the base and BD is the height. Neither of these will

require the distance formula. They can be

A D

C

counted off the graph. AC = 7 and BD = 3

A = ? (7)(3) = 10.5

Practice: Determine the area of DEF. (3 points) b = _______________ h = _______________ A = _______________

To find the area of a triangle the base and height must be horizontal and/or vertical segments. This is not always possible.

Example: Graph GHK with vertices G(2, 5), H(10, 9), and K(6, 1). Find the perimeter and area.

W

H

Perimeter is no different than previously. Use the

distance formula.

G

GH = 8.9, HK = 5.65, GK = 5.65 P = 20.2

YK X

There is a problem finding area. There is no horizontal-

vertical base-height combination.

We will use some "out-of-the-box" thinking.

Surround the triangle with a rectangle so that the

vertices of the triangle are on the sides of the rectangle.

The triangles formed outside the given triangle all have horizontal-vertical base-height

combinations so their areas can be found.

The area of a rectangle is length times width.

A(GHK) = A(rect WHXY) ? A(WHG) ? A(HXK) ? A(GYK)

A(GHK) = 8(8) ? ? (8)(4) ? ? (4)(8) ? ? (4)(4) = 64 ? 16 ? 16 ? 8

A(GHK) = 24

Practice: Graph LMN with vertices L(-3, -3), M(2, 2), and N(5, -5). Find the perimeter and area. Show your work. (8 points)

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