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Learn to find the area of triangles and trapezoids .

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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Learn to find the area of triangles and trapezoids .

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  1. Learn to find the area of triangles and trapezoids.

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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

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