Question

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

CAKE, CA = 5 cm and ∠A = 65°

Answer 1

Given: CA = 5 cm and ∠A = 65°

Rough Diagram


Steps:

1. Drawn a line segment CA = 5 cm.

2. At A on AC, made ∠CAX = 65°

3. With A as centre, drawn arc of radius 5 cm. Let it cut AX at K.

4. With K and C as centres, drawn arcs of radius 5 cm each and let them cut at E.

5. Joined KE and CE.

6. CAKE is the required rhombus.

Calculation of Area:

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

= `1/2 xx 5.4 xx 8.5  "cm"^2`

= 22.95 cm²