You know that the area of a parallelogram is base × height. Using this and the figure, show that the area of a trapezium is half the sum of the parallel sides × height, i.e., 12(a + b)h.

Step-by-step solution

Idea: Cut the trapezium into a parallelogram and a triangle that have the same height h, then add their areas.

1. Draw a line through the end of the top side parallel to the left slant side. It cuts the trapezium into a parallelogram with base a and a triangle whose base is the rest of the bottom side, b − a. Both have height h.1 mark
2. Area of parallelogram = base × height = ah. Area of triangle = 12(b − a)h.1 mark
3. Area of trapezium = ah + 12bh − 12ah = 12ah + 12bh = 12(a + b)h.1 mark

Check: a = 4, b = 10, h = 6: 24 + 12 × 6 × 6 = 42 = 12 × 14 × 6 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Taking the triangle’s base as b instead of b − a.
• Forgetting the 12 for the triangle.

How this can come in the exam

Try one yourself

A trapezium has parallel sides 12 m and 20 m and height 7 m. Find its area by splitting it into a parallelogram and a triangle.

More questions like this

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