Question

what is the area of the shaded triangle? 72 mm² 96 mm² 120 mm² 150 mm²

Explanation:

Step1: Calculate the area of the large triangle

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

Step2: Calculate the area of the un - shaded triangle

The base of the un - shaded triangle is \(6\) mm and the height is \(8\) mm.
\(A_{2}=\frac{1}{2}\times6\times8=24\) \(mm^{2}\)

Step3: Calculate the area of the shaded triangle

Subtract the area of the un - shaded triangle from the area of the large triangle.
\(A = A_{1}-A_{2}=120 - 24=96\) \(mm^{2}\)

Answer:

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