Area of Triangles and Trapezoids 10-2 Area of Triangles and Trapezoids Course 1 Warm Up Problem of the Day Lesson Presentation

Warm Up Evaluate. 1. If the height of a rectangle equals the base of a parallelogram and the base of the rectangle equals the height of the parallelogram, then the rectangle and the parallelogram have the same area. 2. Find the area of a rectangle with a length of 53 in. and a width of 47 in. True 2,491 in2

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Learn to find the area of triangles and trapezoids.

You can divide any parallelogram into two congruent triangles You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram. Height Height Base Base

AREA OF A TRIANGLE The area A of a triangle is half the product of its base b and its height h. 1 2 A = bh h b

Additional Example 1A: Finding the Area of a Triangle Find the area of the triangle. 1 2 A = bh Write the formula. 1 2 Substitute 20 for b and 12 for h. A = (20 · 12) 1 2 A = (240) Multiply. A = 120 The area is 120 ft2.

The legs of a triangle must meet at a 90◦ angle in order to use their lengths as the base and height of the triangle. Caution!

Additional Example 1B: Finding the Area of a Triangle Find the area of the triangle. 1 2 A = bh Write the formula. 1 2 Substitute 30 for b and 24 for h. A = (30 · 24) 1 2 A = (720) Multiply. A = 360 The area is 360 in2.

Find the area of the triangle. Check It Out: Example 1A Find the area of the triangle. 1 2 A = bh Write the formula. 1 2 Substitute 5 for b and 8 for h. A = (5 · 8) 8 in. 1 2 5 in. A = (40) Multiply. A = 20 The area is 20 in2.

Find the area of the triangle. Check It Out: Example 1B Find the area of the triangle. 1 2 A = bh Write the formula. A = 1 2 (4 • 24) Substitute 4 for b and 24 for h. 1 2 24 ft 1 2 A = (108) Multiply. 4 ft 1 2 A = 54 The area is 54 in2.

Additional Example 2: Application The diagram shows the section of a forest being studied. What is the area of the section? 1 2 A = bh Write the formula. 1 2 Substitute 43.9 for b. Substitute 16 for h. A = (43.9 • 16) 1 2 A = (702.4) Multiply. A = 351.2 The area is 351.2 km2.

Substitute 48 for b. Substitute 24.5 for h. A = (48 · 24.5) Check It Out: Example 2 The diagram shows the section of a park being studied. What is the area of the section? 24.5 m 48 m 1 2 A = bh Write the formula. 1 2 Substitute 48 for b. Substitute 24.5 for h. A = (48 · 24.5) 1 2 A = (1176) Multiply. A = 588 The area is 588 m2.

AREA OF A TRAPEZOID b2 The area of a trapezoid is the product of half its height and the sum of its bases. 1 2 A = h(b1 + b2) h b1

Additional Example 3: Finding the Area of a Trapezoid Find the area of the trapezoid. 1 2 A = h(b1 + b2) Use the formula. A = 1 2 · 4(14 + 12 ) Substitute 4 for h, 14 for b1, and 12 for b2. 1 2 A = 1 2 · 4(26 ) A = 53 Multiply. The area is 53 yd2.

Find the area of the trapezoid. Check It Out: Example 3 12 cm Find the area of the trapezoid. 7 cm 16 cm 1 2 A = h(b1 + b2) Use the formula. 1 2 Substitute 7 for h, 16 for b1, and 12 for b2. A = · 7(16 + 12) 1 2 A = · 7(28) A = 98 Multiply. The area is 98 cm2.

Lesson Quiz Find the area of each triangle. 1. 3. 39.9 cm2 2. 84 mi2 Find the area of each trapezoid. 3 4 22.5 m2 4. 113 in2