Question

find the area of the figure shown in the diagram to the nearest hundredth.
a 16.00 m²
b 28.57 m²
c 41.13 m²
d 49.12 m²

Explanation:

Step1: Calculate the area of the square

The side length of the square is \(4m\). The area of a square is \(A = s^2\), so \(A_{square}=4\times4 = 16m^2\).

Step2: Calculate the area of the quarter - circle

The radius of the quarter - circle \(r = 4 + 4=8m\). The area of a full circle is \(A=\pi r^2\), and the area of a quarter - circle is \(A_{quarter - circle}=\frac{1}{4}\pi r^2\). Substitute \(r = 8m\) into the formula: \(A_{quarter - circle}=\frac{1}{4}\times3.14\times8^2=\frac{1}{4}\times3.14\times64 = 50.24m^2\). But wait, no, actually, if we consider the figure as composed of a square of side \(4m\) and two quarter - circles (equivalent to a semi - circle) with radius \(4m\).
The area of the semi - circle: \(A_{semi - circle}=\frac{1}{2}\pi r^2\), with \(r = 4m\), \(A_{semi - circle}=\frac{1}{2}\times3.14\times4^2=\frac{1}{2}\times3.14\times16=25.12m^2\). The area of the square is \(A_{square}=4\times4 = 16m^2\).

Step3: Calculate the total area

The total area \(A=A_{square}+A_{semi - circle}\). Substitute the values: \(A = 16+12.56=28.56\approx28.57m^2\)

Answer:

B. \(28.57m^2\)