Question

what is the area of the shaded triangle?
8 mm
10 mm
6 mm
31 mm
24 mm
72 mm²
96 mm²
120 mm²
150 mm²

Explanation:

Step1: Calculate the area of the large triangle

The base of the large triangle is \(6 + 24=30\) mm and the height is \(8\) mm.
The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\).
So, \(A_{large}=\frac{1}{2}\times30\times8=\frac{1}{2}\times240 = 120\) \(mm^{2}\).

Step2: Calculate the area of the small un - shaded triangle

The base of the small un - shaded triangle is \(6\) mm and the height is \(8\) mm.
Using the area formula \(A=\frac{1}{2}\times base\times height\), we have \(A_{small}=\frac{1}{2}\times6\times8=\frac{1}{2}\times48 = 24\) \(mm^{2}\).

Step3: Calculate the area of the shaded triangle

The area of the shaded triangle \(A_{shaded}=A_{large}-A_{small}\).
\(A_{shaded}=120 - 24=96\) \(mm^{2}\).

Answer:

\(96\space mm^{2}\)