Question

Perimeter of rhombus is 100m and its diagonal is 40m.Find the area of rhombus

Answer 1

$\textbf{Answer:}$

Perimeter of Rhombus =4 x side

$side = \frac{100}{4} = 25$

We know Diagonal of a rhombus divides the rhombus in two equilateral triangle,

$area \: of \: 1 \: equilateral \:triangle.$

$semi \: perimeter = \frac{25 + 25 + 40}{2} = 45$


We will use Heron's Formula here,

$\sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{45(45 - 40)(45 - 25)(45 - 25)} \\ \\ = 300 {m}^{2}$

Area of Rhombus = 300m x 2 = 600m²


$\textbf{Hope it helps you!}$

Answer 2

ANSWER

Perimeter of rhombus =4×side

⇒ 100=4×side

⇒ side=

4

100

⇒ side=25

We know diagonals of a rhombus divides the rhombus in two equilateral triangle.

Now, we are going to find area of 1 equilateral triangle.

Semi perimeter =

2

25+25+40

=45

We will use Heron's formula to find are of equilateral triangle.

⇒ Area of triangle =

s(s−a)(s−b)(s−c)

=

45(45−40)(45−25)(45−25)

=

45×5×20×20

=

90000

=300m

2

⇒ Area of rhombus =2×300m

2

=600m

2

hope it ise full