Question

Construct the following parallelograms with the given measurements and find their area.

EARN, ER = 10 cm, AN = 7 cm and ∠EOA = 110° where `bar("ER")` and `bar("AN")` intersect at O

Answer 1

Given: In the parallelogram EARN,

ER = 10 cm, AN = 7 cm, and LEOA = 110° 

Where `bar("ER")` and `bar("AN")` intersect at O

Rough diagram


Construction:

Steps:

1. Draw a line segment PX. Mark a point O on PX

2. Make an angle ∠EOA = 110° on PX at O

3. Draw arcs of radius 3.5 cm with O as centre on either side of PX. Cutting YZ on A and N

4. With A as centre, draw an arc of radius 10 cm, cutting PX at E. Join AE

5. Draw a line parallel to AE at N cutting PX at R. Join EN and AR

6. EARN is the required parallelogram

Calculation of area:

Area of the Parallelogram EARN = b × h sq.units

= 10 × 5.5

= 55 sq.cm