If the lengths of the sides AB, BC and CA of a triangle

Home » Aptitude » Mensuration » Question

If the lengths of the sides AB, BC and CA of a triangle ABC are 10 cm, 8 cm and 6 cm respectively and if M is the mid - point of BC and MN || AB to cut AC at N, then the area of the trapezium ABMN is equal to

1. 18 sq. cm.
2. 20 sq. cm.
3. 12 sq. cm.
4. 16 sq. cm.

Correct Option: A

∵ 8² + 6² = 10²
∴ ∆ABC is a right angled triangle. CM = MB = 4 cm.
N is the mid point of AC.
∴ CN = 3 cm.
∴ Area of trapezium ABMN
= Area of ∆ABC – Area of ∆CMN

=	1	× 6 × 8 -	1	× 3 × 4
	2		2

= 24 – 6 = 18 sq. cm.