Question

10 A triangle and a parallelogram have the same base and the same area. If the sides of the
triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find
the height of the parallelogram.
​

Answer 1

AnSwer -:



Height of parallelogram = 6 cm

_______________________________
_____________________________

Explanation-:


Area of a triangle-:

“A = √[​s (s-a)(s-b)(s-c)]

S = semi perimeter

A ,B ,C = three sides of triangle

Area of parallelogram-:

“A = b x h”

B = base

H = height

_____________________________

Given ,

The sides of the triangle are

13cm,14cm,15cm

The base of the parallelogram is 14cm

The triangle and the parallelogram have

the same area.

To find,

The height of the rectangle

_______________________________

Area of a triangle-:

“A = √[​s (s-a)(s-b)(s-c)]”

S = semi perimeter

A =13 cm

B = 14 cm

C = 15 cm

Now ,

Semi perimeter-: a + b + c /2

= 13+14+15/2

= 21

Semi perimeter = 21

Then,


√ 21 (21-13)(21-14)(21-15)

= √7506

= 84

Therefore,

Area of triangle-: 84 cm^2

According to the question,

area of parallelogram = area of triangle


Area of parallelogram-: 84 cm^2

Area of parallelogram-:

“A = b x h”

B = base = 14

H = height = ??

Area = 84cm^2

Now ,

14 x h = 84

H = 84/14

H = 6

Hence ,

Height of parallelogram = 6 cm

_______________________________