Preview Warm Up California Standards Lesson Presentation

Warm Up A rectangle has sides lengths of 12 ft and 20 ft. 1. Find the perimeter. 64 ft 2. Find the area. 240 ft2

MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG3.2 California Standards

Additional Example 1: Using Perimeter Find the missing measurement when the perimeter is 71 in. 18 in. 15 in. d 22 in. P = 22 + 15 + 18 + d 71 = 55 + d Substitute 71 for P. -55 -55 Subtract 55 from both sides. 16 = d d = 16 in.

Check It Out! Example 1 Find the missing measurement when the perimeter is 58 in. 14 in. 7 in. d 28 in. P = 28 + 7 + 14 + d 58 = 49 + d Substitute 58 for P. -49 -49 Subtract 49 from both sides. 9 = d d = 9 in.

Additional Example 2: Multi-Step Application A homeowner wants to plant a border of shrubs around her yard that is in the shape of a right triangle. She knows that the length of the shortest side of the yard is 12 feet and the length of the longest side is 20 feet. How long will the border be? Step 1: Find the length of the third side. a2 + b2 = c2 Use the Pythagorean Theorem. 122 + b2 = 202 Substitute 12 for a and 20 for c. 144 + b2 = 400 b2 = 256 b = 16 √256 = 16.

Additional Example 3 Continued Step 2: Find the perimeter of the yard. P = a + b + c = 12 + 20 + 16 Add all sides. = 48 The border will be 48 feet long.

Check It Out! Example 2 A gardener wants to plant a border of flowers around the building that is in the shape of a right triangle. He knows that the length of the shortest sides of the building are 38 feet and 32 feet. How long will the border be? Step 1: Find the length of the third side. a2 + b2 = c2 Use the Pythagorean Theorem. 382 + 322 = c2 Substitute 38 for a and 32 for b. 1444 + 1024 = c2 2468 = c2 c ≈ 49.68 √2468  49.68.

Check It Out! Example 2 Continued Step 2: Find the perimeter of the yard. P = a + b + c  38 + 32 + 49.68 Add all sides.  119.68 The border will be about 119.68 feet long.

area of a triangle or trapezoid have as a factor. A triangle or trapezoid can be thought of as half of a parallelogram. Therefore, the formulas for the area of a triangle or trapezoid have as a factor. 1 2

Additional Example 3: 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 3: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. B. (–1, 1), (4, 1), (4, 4), (0, 4) y Area of a trapezoid A = h(b1 + b2) 1 2 (0, 4) 4 (4, 4) 3 Substitute for h, b1, and b2. (–1, 1) (4, 1) x = • 3(5 + 4) 1 2 5 = 13.5 units2

Graph and find the area of the figure with the given vertices. Check It Out! Example 3 Graph and find the area of the figure with the given vertices. A. (–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. Check It Out! Example 3 Graph and find the area of the figure with the given vertices. B. (–1, 1), (5, 1), (1, 5) Area of a triangle y A = bh 1 2 (1, 5) Substitute for b and h. = • 6 • 4 1 2 4 (–1, 1) (5, 1) = 12 units2 x 6

1. the perimeter of the triangle 36 cm Lesson Quiz 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