Question

In the adjoining figure; if the area of parallelogram ABCD is 90 cm², find :

1. area of parallelogram ABEF.
2. area of ΔABE.

Answer 1

Given: Area (parallelogram ABCD) = 90 cm².

Step-wise calculation:

1. Parallelograms ABCD and ABEF are on the same base AB and between the same pair of parallel lines.

So, they have equal areas.

⇒ Area (parallelogram ABEF)

= Area (parallelogram ABCD) 

= 90 cm²

2. Triangle ABE is exactly half of parallelogram ABEF. 

Diagonal AE divides the parallelogram into two congruent triangles. 

⇒ Area (ΔABE) 

= `1/2` × Area (ABEF)

= `1/2 xx 90`

= 45 cm²