5-Minute Check 1 Find the perimeter of the figure. Round to the nearest tenth if necessary. The area of an obtuse triangle is 52.92 square centimeters.

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5-Minute Check 1 Find the perimeter of the figure. Round to the nearest tenth if necessary. The area of an obtuse triangle is square centimeters. The base of the triangle is 12.6 centimeters. What is the height of the triangle? 13(2) + 11(2) = 48 cm = 37.9 ft = 12.6h  h = 8.4 cm 2 Ch 10.4

Ch 10.4(2) Areas of Trapezoids Standard 10.0 Students compute areas of polygons. Learning Target: I will be able to find the areas of trapezoids. Ch 10.4

Concept 1 Ch 10.4 Theorem 10-4

Example 1 Area of a Trapezoid SHAVING Find the area of steel used to make the side of the razor blade shown below. Area of a trapezoid h = 1, b 1 = 3, b 2 = 2.5 Simplify. Answer: A = 2.75 cm 2 Ch 10.4

Example 1 A.288 ft 2 B ft 2 C ft 2 D.310 ft 2 Find the area of the side of the pool outlined below. Ch 10.4

Example 2 OPEN ENDED Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck. Read the Test Item You are given a trapezoid with one base measuring 4 feet, a height of 9 feet, and a third side measuring 5 feet. To find the area of the trapezoid, first find the measure of the other base. Ch 10.4

Example 2 Solve the Test Item Draw a segment to form a right triangle and a rectangle. The triangle has a hypotenuse of 5 feet and legs of ℓ and 4 feet. The rectangle has a length of 4 feet and a width of x feet. Ch 10.4 OPEN ENDED Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck.

Example 2 Use the Pythagorean Theorem to find ℓ. a 2 + b 2 =c 2 Pythagorean Theorem ℓ 2 =5 2 Substitution 16 + ℓ 2 =25Simplify. ℓ 2 =9Subtract 16 from each side. ℓ=3Take the positive square root of each side. Ch 10.4

By Segment Addition, ℓ + x = 9. So, 3 + x = 9 and x = 6. The width of the rectangle is also the measure of the second base of the trapezoid. Example 2 Area of a trapezoid Substitution Simplify. Answer: So, the area of the deck is 30 square feet. Ch 10.4

Example 2 Check The area of the trapezoid is the sum of the areas of the areas of the right triangle and rectangle. The area of the triangle is or 6 square feet. The area of the rectangle is (4)(6) or 24 square feet. So, the area of the trapezoid is or 30 square feet. Ch 10.4

Example 2 A.58 ft 2 B.63 ft 2 C.76 ft 2 D.88 ft 2 Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed. Ch 10.4

Example 4 A.3 yd B.6 yd C.2.1 yd D.7 yd Trapezoid QRST has an area of 210 square yards. Find the height of QRST. Ch 10.4

Concept 3 Ch 10.4