EXAMPLE 1 Finding Area and Perimeter of a Triangle

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Presentation transcript:

EXAMPLE 1 Finding Area and Perimeter of a Triangle Find the area and perimeter of the triangle. A = bh 1 2 P = a + b + c = (14) (12) 1 2 = 13 + 14 + 15 = 84 in.2 = 42 in.

Finding the Area of a Triangle EXAMPLE 2 Finding the Area of a Triangle Sailboats Find the area of the sail. A = bh 1 2 Write area formula. = (171) (134) 1 2 Substitute values. = 11,457 Multiply. The area of the sail is 11,457 square inches. ANSWER

GUIDED PRACTICE for Examples 1 and 2 A triangle’s height is 9 inches and its base is 10 inches. Find its area. 1. The area of the triangle is 45 in.2. ANSWER

GUIDED PRACTICE for Examples 1 and 2 A triangle’s side lengths are 4 feet, 6 feet, and 2.5 feet. Find its perimeter. The perimeter of the triangle is 12.5 ft. ANSWER

Standardized Test Practice EXAMPLE 3 Standardized Test Practice SOLUTION A = lw Write area formula. 63 = 9w Substitute values. 63 = 93 9 Divide each side by 9. 7 = w Simplify. ANSWER The width is 7 feet. The correct answer is A.

Finding an Unknown Length EXAMPLE 4 Finding an Unknown Length The rectangle at the right has a perimeter of 20 inches. Find the length of the rectangle. p = 2l + 2w Write perimeter formula. 20 = 2l + 2 (4) Substitute 20 for P and 4 for w. 20 = 2l + 8 Multiply. 20 – 8 = 2l + 8 – 8 Subtract 8 from each side. 12 = 2l Simplify.

Finding an Unknown Length EXAMPLE 4 Finding an Unknown Length 2l 2 12 = Divide each side by 2. 6 = l Simplify. ANSWER The length of the rectangle is 6 inches.

EXAMPLE 5 Using an Area Formula Zoo Exhibit A polar bear exhibit includes a rectangular pool and rocks. Find the area of the region with rocks. SOLUTION Let r be the area of the region with rocks.

The area of the region with rocks is 1600 square feet. ANSWER EXAMPLE 5 Using an Area Formula 40 56 = 20 32 + r 2240 = 640 + r Write an algebraic model. 2240 – 640 = 640 – 640 + r Subtract 640 from each side. 1600 = r Simplify. The area of the region with rocks is 1600 square feet. ANSWER

GUIDED PRACTICE for Examples 3, 4 and 5 Find the unknown dimension. 3. Perimeter = 36 feet ANSWER The length of the rectangle is 10 ft.

GUIDED PRACTICE for Examples 3, 4 and 5 Area = 32 mm2 4. ANSWER Height of the triangle is 8 mm.

GUIDED PRACTICE for Examples 3, 4 and 5 Area = 6 in.2 ANSWER Base of the triangle is 3 in.

GUIDED PRACTICE for Examples 3, 4 and 5 6. What If? In Example 5, suppose the length of the exhibit area was 64 feet instead of 56 feet. Find the area of the region with rocks. ANSWER The area of the region with rock is 1920 ft2.