Grade 6 Geometry: Area of Quadrilaterals

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A trapezoid has parallel bases of 9 ft and 17 ft and a height of 11 ft. What is its area in square feet?

   1. Area of a trapezoid = ½ × (base 1 + base 2) × height.
   2. Add the parallel bases: 9 + 17 = 26.
   3. Multiply by the height: 26 × 11 = 286.
   4. Take half: 286 ÷ 2 = 143. The area is 143 square feet.

   Answer: 143

2. Example 2

   A parallelogram has a base of 6.5 m, a slanted side of 11 m, and a height of 7 m. What is its area in square meters?

   1. Area of a parallelogram = base × height. Use the straight-up height (7 meters), not the slanted side (11 meters).
   2. 6.5 × 7 = 45.5.
   3. The area is 45.5 square meters.

   Answer: 45.5

3. Example 3

   A parallelogram has an area of 42 square meters and a base of 7 m. What is its height in meters?

   1. Area = base × height, so height = area ÷ base.
   2. 42 ÷ 7 = 6.
   3. Check: 7 × 6 = 42. The height is 6 meters.

   Answer: 6