Question

34
Find the area of a rhombus whose perimeter is 80 m and one of
whose diagonal is 24 m.​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Here,

Perimeter of rhombus = 80m

One diagonal = 24m

Assume,

PQRS be rhombus and diagonal QS = 24m

So,

Area of ∆QRS = Area of ∆PQS

Perimeter of rhombus (PQRS) = 4 × side

80 = 4 × side

Side = 80/4

Side = 20 m

Side (PQ = QR = RS = SP)

= 20 m

So,

Semi perimeter = (a + b + c)/2

ΔQRS(s) = (20 + 20 + 24)/2

s = 64/2 m

s = 32 m

So,

Using heron formula :-

Area of ΔQRS,

A = √s(s - a)(s - b)(s - c)

A = √32(32 - 20) × (32 - 20) × (32 - 24)

A = √32 × 12 × 12 × 8

A = √(32 × 8) × (12 × 12)

A = √256 × (12 × 12)

A = √(16 × 16) × (12 × 12)

A = 16 × 12

A = 192 m²

Area of ΔQRS = 192 m²

Area of ΔQRS = Area of ΔPQS = 192 m²

Area of rhombus PQRS :-

= 2 × Area of ∆QRS

= 2 × 192

= 384 m²

Therefore,

Area of rhombus = 384 m²