Question

Construct the following quadrilaterals with the given measurements and also find their area.

AGRI, AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°

Answer 1

AG = 4.5 cm, GR = 3.8 cm, ∠A = 60°, ∠G = 110° and ∠R = 90°


Steps:

1. Draw a line segment AG = 4.5 cm

2. At G on AG made ∠AGX = 110°

3. With G as centre drawn an arc of radius 3.8 cm let it cut GX at R.

4. At R on GR made ∠GRZ = 90°

5. At A on AG made ∠GAY = 90°

6. AY and RZ meet at I.

7. AGRI is the required quadrilateral.

Calculation of Area:

Area of the quadrilateral AGRI = `1/2 xx "d" xx ("h"_1 + "h"_2)  "sq.units"`

= `1/2 xx 6.8 xx (2.9 + 2.4)  "cm"^2`

= `1/2 xx 6.8 xx 5.3 xx "cm"^2`

Area of the quadrilateral = 18.02 cm²