Question

11. Find the area of a parallelogran whose sides
are 33 cm and 39 cm and diagonal is 60cm​

Answer 1

Given,

A parallelogram whose sides are 33 cm and 39 cm and diagonal is 60 cm.

To Find,

The area of the parallelogram.

Solution,

We know that the diagonal of a parallelogram divides it two 2 congruent triangles with same base and equal area.

Therefore we can say that:

Area of parallelogram = 2 x each triangle made by the diagonal.

Given,

Side 1 (a) = 33 cm

Side 2 (b) = 39 cm

Diagonal (c) = 60 cm

Semiperimeter, S = a+b+c/2 = 33+39+60/2 = 66.

By applying Heron's formula,

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

$A =\sqrt{66(66-33) (66-39) (66-60)}$

$A= \sqrt{66*33*27*6}$

$A=\sqrt{6*11*3*11*3*3*3*6}$

A = 6 x 11 x 3 x 3

A = $594cm^2$

Therefore, the area of the parallelogram is 2 x 594 = $1188cm^2$.

Formulas used:

→ Heron's formula

Note:

The symbol * refers to the multiplication sign 'x'.