Question

The sides of a parallelogram are 100m each and length of the longest diagonal is 160 m find the area

Answer 1

Answer:

9600 sq cm

Step-by-step explanation:

Length of diagonal, BD = 2*[100^2-(160/2)^2]^0.5

= 120 cm.

Area of rhombus = AC*BD/2 = 160*120/2

= 9600 sq cm.

Answer 2

Given,

Each side of the parallelogram a = 100m.

To Find,

The parallelogram's area.

Solution,

Given that,

Each side a = 100m

Diagonal length d = 160m.

The diagonal will make two triangles.

The triangle sides will be

100m, 100m, 160m.

The perimeter of the triangle S=

$\frac{a+b+c}{2}$ = $\frac{100+100+160}{2}$

180m

Heron's equation.

Area A = $\sqrt{S(S-a)(S-b)(S-c)}$

$\sqrt{180(180-100)(180-100)(180-160)}$

$\sqrt{23040000}$ = 4800m²

Therefore area of a parallelogram

2* 4800= 9600m²

The area of the parallelogram is 9600m².