A triangle and a parallelogram have the same base and same area. If th

1.	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» Answer: 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 = √s(s - a)(s - b)(s - c) = √42(42 - 30)(42 - 28)(42 - 26) = √42 × 12 × 14 × 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.

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»

Answer:

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 = √s(s - a)(s - b)(s - c)

= √42(42 - 30)(42 - 28)(42 - 26)

= √42 × 12 × 14 × 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.