Question

which value is closest to the area of the following figure, in square millimeters? 79 mm² 92 mm² 67 mm² 29 mm²

Explanation:

Step1: Calculate the area of the semicircle

The formula for the area of a circle is \(A = \pi r^{2}\). For a semicircle, the area \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Given the diameter \(d = 6\) mm, so the radius \(r=\frac{d}{2}=3\) mm. Then \(A_{semicircle}=\frac{1}{2}\times\pi\times3^{2}=\frac{9\pi}{2}\approx\frac{9\times3.14}{2}=14.13\) \(mm^{2}\).

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, the base \(b = 6\) mm and the height \(h = 5\) mm. So \(A_{triangle}=\frac{1}{2}\times6\times5=15\) \(mm^{2}\).

Step3: Calculate the total area

The total area \(A = A_{semicircle}+A_{triangle}\). \(A\approx14.13 + 52.98=67.11\) \(mm^{2}\).

Answer:

\(67\ mm^{2}\)