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Section 10.2 – Area: Triangles and Trapezoids

Learn how to find the area of triangles and trapezoids using the base and height. Includes examples and practice problems.

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Section 10.2 – Area: Triangles and Trapezoids

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  1. Section 10.2 – Area: Triangles and Trapezoids pages 527 - 531

  2. In section 9.3, we learned how to name a triangle by its sides and angles.

  3. The Bermuda Triangle is a triangular region between Bermuda, Florida, and Puerto Rico.

  4. Last week we learned how to find the area of parallelograms.  Today we are going to discuss how to find the areas of triangles and trapezoids.  When looking at a parallelogram, we notice that the diagonal of a parallelogram divides the parallelogram into two congruent triangles.   Thus, the area of each triangle is half the area of the parallelogram.

  5. The area of a triangle equals half the product of any base length b and the corresponding height h.

  6. Example 1: Find the area of the triangle. The area is 12 cm2.

  7. . Check Understanding: a. Find the area of the triangle. b. Find the area of the triangle.

  8. Example 2: How much siding does a builder need to cover the side of the house shown at the left? Add to find the total: 72 + 160 = 232. The builder needs 232 ft2 of siding.

  9. A parallelogram can be divided into two congruent trapezoids.  The area of each trapezoid is one-half the area of the parallelogram. The two parallel sides of a trapezoid are its bases.  If we call the longer side b1 and the shorter side b2, then the base of the parallelogram is b1+b2.

  10. Area of a Trapezoid The area of a trapezoid is half the product of the height and the sum of the lengths of the bases. A = ½ h(b1 + b2)

  11. Example 3: Finding area of a trapezoid The Erie Canal opened in 1825 and was hailed as an engineering marvel. Below is a cross section of the Erie Canal. Find the area of the trapezoidal cross section. The area of the cross section is 136 ft2.

  12. . . Check Understanding a. Find the area of the trapezoid.             b. Find the area of the trapezoid.                     

  13. Homework • pages 530 - 531 • #s 1-10, 20-28 • DRAW DIAGRAMS and • write problems and answers, EXCEPT for word problems and multiple-choice problems • SHOW ALL WORK! • failure to write problems and/or show work will result in either receiving partial or no credit

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