Question

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

PQRS, PQ = QR = 3.5 cm, RS = 5.2 cm, SP = 5.3 cm and ∠Q = 120°

Answer 1

Given PQ = QR = 3.5 cm, RS = 5.2 cm, SP = 5.3 cm and ∠Q = 120°


Steps:

1. Draw a line segment PQ = 3.5 cm

2. Made ∠Q = 120°. Drawn the ray QX.

3. With Q as centre drawn an arc of radius 3.5 cm. Let it cut the ray QX at R.

4. With R and P as centres drawn arcs of radii 5.2 cm and 5.5 cm respectively and let them cut at S.

5. Joined PS and RS.

6. PQRS is the required quadrilateral.

Calculation of Area:

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

= `1/2 xx 6 xx (4.3 + 1.7)  "cm"^2`

= 3 × 6 cm²

= 18 cm²

Area of the quadrilateral PQRS = 18 cm²