Question

Let ABCD be a parallelogram such that AB = 10 , BC = 14, and Angle A = 45. Find the area of the parallelogram. Please do not answer in decimal form. Answer using a square root

Answer 1

70√2 units²

Explanation:

(see attached for reference notes on parallelograms)

we are given ABCD is a parallelogram where

Short Length, AB = 10 units

Long Length, BC = 14 units

Angle A = 45°

The area of the parallelogram is hence,

= AB x BC sin 45°

= 10 x 14 x sin 45

= 140 sin 45° (recall from special angles, that sin 45° = 1/√2)

= 140/√2 (remove radical from denominator by multiplying by √2/√2)

= (140/√2) x (√2/√2)

=70√2 units²