Question

In Figure 1, a parallelogram is drawn in a trapezium. If the area of the parallelogram is 390 cm², find the area of the trapezium.​

Answer 1

Explanation:

the area of the parallelogram is

baseline × height.

we know the baseline (15 cm), because as parallelogram it must have 2 pays off equal sides. so, the bottom side must be 15 cm too.

15×height = 390

height = 390/15 = 26 cm

now, the height of the triangle on the right is the same height.

and the baseline of this triangle is 25 - 15 = 10 cm.

the area of a triangle is

baseline × height / 2

so, in our case

10 × 26 / 2 = 10×13 = 130 cm²

therefore the area of the trapezium is the area of the parallelogram plus the area of the triangle :

390 + 130 = 520 cm²