Question

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

Answer 1

$\large\fcolorbox{red}{yellow}{Answer}$

Height=12 cm

Step-by-step explanation:

First Lets Find Area of Triangle :-

• Side 1 (a) = 26 cm
• Side 2 (b) = 30 cm
• Side 3 (c) = 28 cm

$s = \frac{perimeter}{2} \\ => \frac{26 + 28 + 30}{2} \\ => \frac {84}{2} \\ => \boxed{42}$

Area of triangle by Heron's Formula :-

$\bf\color{orange}{\sqrt{s(s-a)(s-b)(s-c)}}$

Lets Put The Values :-

$=>\sqrt{42(42-26)(42-28)(42-30)} <strong> </strong><strong> </strong> \\ =>\sqrt{42 \times 16 \times 14 \times 12} \\ => \sqrt{(7 \times 6) \times 16 \times (7 \times 2) \times ( 6 \times 2)} \\ => \sqrt {16 \times 7 \times 7 \times \ 2 \times 2 \times 6 \times 6} \\ => 4 \times 7 \times 2 \times 6 \\ => \boxed {336}$

Thus The Area Of Triangle is 336 cm²

Area Of triangle = Area Of parallelogram

Therefore The Height of Parallelogram :-

• Base = 28 cm
• Area = 336 cm
• Height = ?

Formula :-

$\bf\color{blue}{Area = Base \times Height}$

Lets Put The values :-

$=>336 = 28 \times Height \\ => Height = \frac{336}{28} \\ => \boxed{12}$

Thus The Height Is 12 cm