Question

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

Answer 1

☆ Height of the parallelogram = 12 cm ☆

Step-by-step explanation:

Given:

• Triangle and Parallelogram has the same base and same area
• Sides of the triangle: 26 cm, 28 cm, and 30 cm.
• Parallelogram stands on the base 28 cm.

To find:

• Height of the parallelogram

Solution:

☯ The perimeter of the triangle is calculated as the sum of all three sides of the triangle.

$\implies{\rm}$ P = a + b + c

$\implies{\rm}$ P = 26 + 28 + 30

$\implies{\rm}$ P = 84 cm

☯ Semi perimeter is also considered as half of the perimeter.

$\implies{\rm}$ s = P/2

$\implies{\rm}$ s = 84/2

$\implies{\rm}$ s = 42 cm

☯ By applying Heron's formula, we can find the area of the triangle.

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

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

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

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

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

$\sf{\implies A = 336\:cm^2}$

☯ According to the question, we are given that area of the parallelogram and triangle are equal.

$\implies{\rm}$ Area of parallelogram = Area of triangle

$\implies{\rm}$ Base × Height = 336

$\implies{\rm}$ 28 × Height = 336

$\implies{\rm}$ Height = 336/28

$\implies{\rm}$ Height = 12 cm

☯ Hence, the height of the parallelogram is 12 cm.