Question

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

PARK, PR = 9 cm and ∠P = 70°

Answer 1

Given: PR = 9 cm and ∠P = 70°

Rough Diagram


Steps:

1. Drawn a line segment PR = 9 cm.

2. At P, made ∠RPX ∠RPY = 35° on either side of PR.

3. At R, made ∠PRQ = ∠PRS = 35° on either side of PR

4. Let PX and RQ cut at A and PY and RS at K.

5. PARK is the required rhombus

Construction of Area:

Area of the rhombus = `1/2 xx "d"_1 xx "d"_2  "sq.units"`

= `1/2 xx 9 xx 6.2  "cm"^2`

= 27.9 cm²