Mr. Peter Richard P.R Find the Area and Perimeter of Perimeter and Area of Triangles, Quadrilaterals, and Trapezoids P.R Find the Area and Perimeter of Quadrilaterals, Triangles, and Trapezoids. Mr. Peter Richard Will make sure you don’t get trapped in a Trapezoid made by some Square Triangle. Algebra 1

Additional Example 1: Finding the Perimeter of Triangles and Trapezoids Find the perimeter of each figure. A. 7 Add all sides. 4 P = 4 + 7 + 10 10 = 21 units 17 8 11 6 Add all sides. B. P = 8 + 11 + 6 + 17 = 42 units

AREA OF A TRIANGLE Words Numbers Formula Triangle: The area A of a triangle is one-half the base length b times the height h. A = (8)(4) = 16 units2 Think of a Triangle as half of a Rectangle 1 2

Triangle Area = ½ bh ( ‘h’ is the vertical height) b b

Area of Parallelograms Height – * The altitude of the //-ogram. * Line from a vertex of the //-ogram  to the opposite side. Base – Is any of its sides. A = bh Area of a //-ogram * units 2 Height Base

Example 1: Find the area of the following //-ogram. A = bh = (12m)(8m) = 96m2 Perimeter? 12 + 10.5 + 12 + 10.5 = 45m

A triangle or trapezoid can be thought of as half of a parallelogram.

AREA OF A TRAPEZOID Words Numbers Formula Trapezoid: The area is ½ times the height h times the sum of the bases (b1 +b2) Bases = two Parallel Sides A = (h)(b1 + b2) 1 2 A = (2)(3 + 7) = 10 units2 1 2

Additional Example 2A: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. A. (–2, 2), (4, 2), (0, 5) Area of a triangle y A = bh 1 2 (0, 5) Substitute for b and h. = • 6 • 3 1 2 3 (–2, 2) (4, 2) 6 = 9 units2 x

Additional Example 2B: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. B. (–1, 2), (5, –2), (5, 2), (–1, 6) y (–1, 6) Area of a trapezoid A = h(b1 + b2) 1 2 (5, 2) Substitute for h, b1, and b2. 8 6 4 x = • 6(8 + 4) 1 2 (–1, –2) (5, –2) = 36 units2

Graph and find the area of the figure with the given vertices. Try This: Example 2A Graph and find the area of the figure with the given vertices. A. (–1, 1), (1, 7), (7, 1) Area of a triangle y (1, 7) A = bh 1 2 Substitute for b and h. 6 = • 8 • 6 1 2 (7, 1) (–1, 1) = 24 units2 x 8

Graph and find the area of the figure with the given vertices. Try This: Example 2B Graph and find the area of the figure with the given vertices. B. (–2, –1), (0, 5), (3, 5), (5, –1) y Area of a trapezoid 3 7 6 (3, 5) (0, 5) A = h(b1 + b2) 1 2 Substitute for h, b1, and b2. x = • 6(7 + 3) 1 2 (–2, –1) (5, –1) = 30 units2

Find the shaded area Area of square = 10 x 10 = 100 cm2 10cm A. of triangle = ½ x 3 x 4 = 6 cm2 Shaded area = 100 – 6 = 94 cm2 10cm 3cm 3cm 4cm

Problem #19 The tree farm needs fertilizing. Each box of fertilizer covers 36 square feet. About how many boxes of fertilizer are needed?

Because the path is 1 ft wide, increase each side Margaret’s garden is a square 12 ft on each side. Margaret wants a path 1 ft wide around the entire garden. What will the outside perimeter of the path be? Because the path is 1 ft wide, increase each side of the garden by 1 ft. s = 1 + 12 + 1 = 14 P = 4s Formula for perimeter of a square P = 4(14) = 56 Substitute 14 for s. The perimeter is 56 ft. 1-7

1. Find the perimeter in inches. 2. Find the area in square feet. 3. How many bags of fertilizer would cover the area if each bag covers 2 Sq. FT? 4. Find the perimeter of a triangle whose vertices are X(–6, 2), Y(8, 2), and Z(3, 14). 5. Find the area of the figure below. All angles are right angles. A rectangle is 9 ft long and 40 in. wide. 296 in. 30 ft2 81 cm2 42 units 256 in.2 PR

Lesson Homework Use the figure to find the following measurements. 1. The perimeter of the triangle 36 cm 2. The perimeter of the trapezoid 44 cm 3. The perimeter of the combined figure 64 cm 4. The area of the triangle 54 cm2 5. The area of the trapezoid 104 cm2