Question

A dance floor has to be built as a triangular glass platform with the dimensions 7 m, 8 m and 9 m. The total surface area of the glass required to build such a platform is equal to ___$m^2$.

• A. $5\sqrt{5}$
• B. 5
• C. $12\sqrt{5}$
• D. 6

Answer 1

The correct option is C

$12\sqrt{5}$

Let, a, b & c be the sides of the triangle.
a = 7 m, b = 8 m and c = 9 m
$\text{Semi-perimeter of a triangle,}s=\frac{a+b+c}{2}s=\frac{7+8+9}{2}=\frac{24}{2}=12m\text{Heron's formula for area of triangle,}A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{\left(12\right)(12-7)(12-8)(12-9)}A=\sqrt{\left(12\right)\left(5\right)\left(4\right)\left(3\right)}=12\sqrt{5}{m}^2$