Question

A triangle and a parallelogram have the same base and the same area. If the sides of
the triangle are 26 cm. 28 cm ana 30 cm, and the parallelogram stands on the base
28 cm, find the height of the parallelogram.​

Answer 1

• Given:

1. A triangle and a parallelogram with Same Base and Same Area
2. A triangle with1st side = 26 cm 2nd side = 28 cm 3rd side = 30 cm
3. A parallelogram withBase = 28 cm

• What To Find:

We have to find The height of the parallelogram.

• How To Find:

To find the height, we have to,

First, find the area of the triangle using a certain formula.

Next, find the height of the parallelogram using a certain formula.

• Formulas Needed:

For the area of a triangle -

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

Where,

s = Semi-perimeter

a = 1st side

b = 2nd side

c = 3rd side

For the area of a parallelogram -

$\bf \longmapsto Area = b \times h$

Where,

b = Base

h = Height

• Solution:

Finding the area of the triangle.

Finding the semi-perimeter.

⇒ Perimeter = Sum of three sides.

⇒ Perimeter = 26 + 28 + 30

⇒ Perimeter = 84 cm

⇒ Semi-perimeter = Perimeter ÷ 2

⇒ Semi-perimeter = 84 ÷ 2

⇒ Semi-perimeter = 42 cm

Finding the area.

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

$\sf \implies Area = \sqrt{42(42-26)(42-28)(42-30)}$

$\sf \implies Area = \sqrt{42(16)(14)(12)}$

$\sf \implies Area = \sqrt{112896}$

$\sf \implies Area = 336 \: cm^2</p><p>$

• Finding the height of the parallelogram.

⇒ Area of the triangle = Area of the parallelogram = 336 cm²

⇒ Area = b × h

⇒ 336 cm² = 28 × h

⇒ 336 ÷ 28 = h

⇒ 12 cm = h

Final Answer:

∴ Thus, the height of the parallelogram is 12 cm.

Answer 2

$\sf\huge\red{Answer:)}$

Given:-

Area of the parallelogram = Area of the triangle

By using the area of the parallelogram formula, we can calculate the height of the parallelogram

By using Heron’s formula,

we can calculate the area of a triangle.

Heron's formula for the area of a triangle

is: Area

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

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle.

For ∆ABE, a = 30 cm, b = 26 cm, c = 28 cm

Semi Perimeter: (s) = Perimeter/2

s = (a + b + c)/2

= (30 + 26 + 28)/2

= 84/2

= 42 cm

By using Heron’s formula,

Area of a ΔABE

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

$= \sqrt{42(42 - 30)(42 - 28)(42 - 26)}$

$= \sqrt{42 \times 12 \times 14 \times 16}$

= 336 cm2

Area of parallelogram ABCD = Area of ΔABE (given)

Base × Height = 336 cm2

28 cm × Height = 336 cm2

On rearranging, we get

Height = 336/28 cm = 12 cm

Thus, height of the parallelogram is 12 cm.