Math, asked by Gangotri4967, 1 year ago

If the lengths of the sides of a parallelogram are 13 cm and 10 cm and the length of one of its diagonal is 9 cm, then find its area.

Answers

Answered by hukam0685
5

Answer:

Area of || gm ABCD= 89.79 sq-cm

Step-by-step explanation:

As we know that area of a parallelogram is

\boxed{Area \: of \: parallelogram = base \times perpendicular \: height} \\  \\

But here perpendicular height is not given in the question.

See the figure attached, here we come to know that a diagonal divides the parallelogram into two equal triangles.

Area of || gm = ar(∆ADC)+ar(∆ABC)

Since ∆ADC is congruent to ∆ABC

So

Area of || gm = 2 × ar(∆ADC)

As we know that when sides are given we can calculate the area of triangle by Heron's Formula

a=13 cm

b= 10 cm

c= 9 cm

S =  \frac{13 + 10 + 9}{2}  \\  =    \frac{32}{2}  \\  \\  = 16 \\  \\

 =  \sqrt{16(16 - 13)(16 - 10)(16 - 9)}  \\  \\  =  \sqrt{16 \times 3 \times 6 \times 7}  \\  \\  = 12 \sqrt{14}  \:  \:  {cm}^{2}  \\  \\

Area of || gm =

2 \times 12 \sqrt{14}  \\  \\  = 24 \sqrt{14}  \\  \\  = 89.79 \:  {cm}^{2}  \\  \\

Hope it helps you

Attachments:
Similar questions