Question

a field is in the shape of a rhombus whose perimeter is 400m and one of its diagonal is 160m, find the area of the field

Answer 1

Perimeter = 400 m (Given)

Find the length:

Perimeter = 4 x Length

4 x Length = 400

Length = 400 ÷ 4 = 100 m

Find half of the other diagonal:

a² + b² = c²

a² + (160 ÷ 2)² = 100²

a² + 80² = 100²

a² = 100² - 80²

a² = 3600

a = √3600

a = 60 m

Find the diagonal:

diagonal = 60 x 2 = 120 m

Find the area:

Area = 1/2 ( diagonal 1 x diagonal 2 )

Area = 1/2 (160 x 120) = 9600 m²

Answer: The area is 9600 m²

Answer 2

Perimeter=4*a

400=4*a

100=a

S=a+b+c/2

100+100+160/2

360/2

180

Area=√s(s-a)(s-b)(s-c)

√180(180-100)(180-100)(180-160)

√180*80*80*20

4800m²

Area of field =4800*2

9600m²

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