Question

A field is in the form of a rhombus whose area is 216cm2 and height is 16cm. Find the area of a square field whose side is equal to the height of the rhombus. Also, find the difference in their perimeters.]

Answer 1

given :-

area of the rhombus shaped field = 216cm²

it's height = 16cm

formula to find the area of a rhombus shaped field is base × height where base is the side of the rhombus.

➡ base × height = 216cm²

➡ base × 16 = 216cm²

➡ base = 216/16

➡ base = 13.5cm

therefore the side of the rhombus is 13.5cm.

it's perimeter = 4 × side

= 4 × 13.5

= 54cm

now ATQ,

we've to find the area of a square field whose side = height of the rhombus

➡ side of the square field = 16cm

it's area = side × side

= 16 × 16

= 256cm²

it's perimeter = 4 × side

= 4 × 16

= 64cm

we can clearly see that the perimeter of square field is greater by = 64 - 54 = 10cm

hence, the difference between their perimeter is 10cm.

Answer 2

$\bold {\huge {Your ~answer :-}}$

$\bf\huge\boxed{256cm^2,\:10cm}$

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Given—

Area of the rhombus = 216cm²

height = 16cm

We know that

Area of rhombus = base× height

=>base × height = 216cm²

=> base × 16 = 216cm²

=> base = 216/16

=> base = 13.5cm

therefore the side of the rhombus is 13.5cm.

Perimeter of rhombus = 4 × side

= 4 × 13.5

= 54cm

A/q

we've to find the area of a square field whose side = height of the rhombus

=> side of the square field = 16cm

area of square = side × side

= 16 × 16

= 256cm²

perimeter of square = 4 × side

= 4 × 16

= 64cm

Therefore the difference between perimeter of square and rhombus= 64 - 54 = 10cm

HENCE, the difference between their perimeter is 10cm.

$\huge{\red{\ddot{\smile}}}$