Question

A triangle and a parallelogram stand
on the same base and are equal in area. If the sides of the triangle 40cm,24cm
and 32cm and the base of the parallelogram is 40cm, find the
corresponding height of the parallelogram
​

Answer 1

Answer:

Step-by-step explanation:

Answer :-

Given:-

A triangle and a parallelogram standon the same base and are equal in area.

Sides of the triangle 40cm,24cm

and 32cm.

Bases measure 40 cm.

We need:-

Corresponding height of the parallelogram.

Theorem:- Triangles and Parallelograms on same base are equal in Area (1)

Heron's Formula

Let's Do!

s = s1+s2+s3/2

Where s1, s2 and s3 are sides.

Then, semi perimeter or s will be:-

40+24+32/2

= 96/2

= 48 cm.

Now,

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

Where s-a = 48 - 40 = 8

Where s-a = 48 - 32 = 16

Where s-a = 48 - 24 = 24

$\sf{Area = \sqrt{ 48(8)(16)(24)}}$

= 384 cm²

Now, b × h = 384

Height = 384/40 = 9.6 cm.

Answer 2

Answer:

Step-by-step explanation:

Answer :-

Given:-

A triangle and a parallelogram standon the same base and are equal in area.

Sides of the triangle 40cm,24cm

and 32cm.

Bases measure 40 cm.

We need:-

Corresponding height of the parallelogram.

Theorem:- Triangles and Parallelograms on same base are equal in Area (1)

Heron's Formula

Let's Do!

s = s1+s2+s3/2

Where s1, s2 and s3 are sides.

Then, semi perimeter or s will be:-

40+24+32/2

= 96/2

= 48 cm.

Now,

Area= s(s−a)(s−b)(s−c)

Where s-a = 48 - 40 = 8

Where s-a = 48 - 32 = 16

Where s-a = 48 - 24 = 24

Area= 48(8)(16)(24)

= 384 cm²

Now, b × h = 384

Height = 384/40 = 9.6 cm.