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This lesson teaches you how to find the area of triangles and trapezoids using simple formulas and substituting values. Examples and applications are provided.
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You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram.
Additional Example 1A: Finding the Area of a Triangle Find the area of the triangle. 1 2 bh A = Write the formula. 1 2 Substitute 20for b and 12for h. (20· 12) A = 1 2 Multiply. (240) A = A = 120 The area is 120 ft2.
Reading Math An altitude of a triangle is a perpendicular segment from one vertex to the line containing the opposite side. The length of the altitude is the height.
Additional Example 1B: Finding the Area of a Triangle Find the area of the triangle. 1 2 bh A = Write the formula. 1 2 Substitute 30for b and 24for h. (30· 24) A = 1 2 Multiply. (720) A = A = 360 The area is 360 in2.
Check It Out: Example 1A Find the area of the triangle. 1 2 bh A = Write the formula. 1 2 Substitute 5for b and 8for h. (5· 8) A = 8 in. 1 2 5 in. Multiply. (40) A = A = 20 The area is 20 in2.
1 2 Substitute 4 for b and 24for h. 1 (4 • 24) A = 1 2 2 1 2 Check It Out: Example 1B Find the area of the triangle. 1 2 bh A = Write the formula. 24 ft 1 2 Multiply. (108) A = A = 54 4 ft 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 bh A = Write the formula. 1 2 Substitute 43.9for b. Substitute 16for h. (43.9 •16) A = 1 2 Multiply. (702.4) A = A = 351.2 The area is 351.2 km2.
24.5 m 48 m Check It Out: Example 2 The diagram shows the section of a park being studied. What is the area of the section? 1 2 bh A = Write the formula. 1 2 Substitute 48for b. Substitute 24.5for h. (48· 24.5) A = 1 2 Multiply. (1176) A = A = 588 The area is 588 m2.
1 2 Substitute 4 for h, 14 for b1, and 12 for b2. · 4(14 + 12 ) A = 1 2 1 2 1 2 · 4(26 ) 1 A = 2 Additional Example 3: Finding the Area of a Trapezoid Find the area of the trapezoid. 1 2 h(b1 + b2) Use the formula. A = A = 53 Multiply. The area is 53 yd2.
Check It Out: Example 3 12 cm Find the area of the trapezoid. 7 cm 16 cm 1 2 h(b1 + b2) Use the formula. A = 1 2 Substitute 7 for h, 16 for b1, and 12 for b2. · 7(16 + 12) A = 1 2 · 7(28) A = A = 98 Multiply. The area is 98 cm2.