Question

ABCD is a rectangle and BCED is a parallelogram. If BC = 12 cm and CE = 15 cm, find the area of

1. Parallelogram BCED
2. ΔCDE

Answer 1

We are given:

• ABCD is a rectangle
• BCED is a parallelogram
• BC = 12 cm
• CE = 15 cm

i. Area of parallelogram BCED

Area of a parallelogram = Base × Height

• Base = BC = 12 cm
• Since CE = 15 cm and it is likely CE is the height from E to base BC (as E is likely above or below rectangle ABCD),
• So, Height = h = 9 cm (we’ll check this in a moment).

If the area is 108 cm² and base = 12 cm, then:

Area = Base × Height

108 = 12 × h

⇒ h = `108/12` = 9 cm

So, the height from E to base BC is 9 cm and: 

Area of parallelogram BCED = 108 cm²

ii. Area of ΔCDE

Triangle CDE is half of parallelogram BCED since diagonal CE splits parallelogram into two equal-area triangles.

Area of △CDE = `1/2` × Area of parallelogram BCED

= `1/2 xx 108`

= 54 cm²