Question

find the area of the figure pictured. * 55 mm 32.5 mm 12.5 mm 12.5 mm your answer

Explanation:

Step1: Divide the figure into parts

The figure can be divided into a quarter - circle, a square, and a right - triangle.

Step2: Calculate the area of the quarter - circle

The radius of the quarter - circle $r = 12.5$ mm. The area of a full - circle is $A_{circle}=\pi r^{2}$, so the area of a quarter - circle $A_{1}=\frac{1}{4}\pi r^{2}=\frac{1}{4}\pi\times(12.5)^{2}=\frac{156.25\pi}{4}\text{ mm}^2$.

Step3: Calculate the area of the square

The side length of the square $s = 12.5$ mm. The area of the square $A_{2}=s^{2}=(12.5)^{2}= 156.25\text{ mm}^2$.

Step4: Calculate the base of the right - triangle

The base of the right - triangle $b=55 - 12.5=42.5$ mm and the height $h = 12.5$ mm. The area of a right - triangle is $A_{3}=\frac{1}{2}bh=\frac{1}{2}\times42.5\times12.5=\frac{531.25}{2}\text{ mm}^2$.

Step5: Calculate the total area

$A = A_{1}+A_{2}+A_{3}=\frac{156.25\pi}{4}+156.25+\frac{531.25}{2}$.
$A=\frac{156.25\times3.14}{4}+156.25 + 265.625$.
$A=\frac{490.625}{4}+156.25+265.625$.
$A = 122.65625+156.25+265.625$.
$A=544.53125\text{ mm}^2$.

Answer:

$544.53125\text{ mm}^2$