Question

Find the area of the shaded part in the figure: (Use π=3.14)

Answer 1

Hint: we will find the diagonal AC, since, AC represents the diameter of the circle. The radius of the circle is half of the diameter. From the radius, we found out we will find the area of the circle shown. Also, find the area of the rectangle from the given graph.
from the subtraction of the area of the rectangle from the area of the circle, we will get the area of the shaded portion.
Given: AD= 5cm, DC= 12cm
Formulas used:
Pythagoras theorem formula; \[\text{hypotenuse}{{\text{e}}^{2}}=\text{side}_{1}^{2}+\text{side}_{2}^{2}\]
Area of circle \[=\pi {{r}^{2}}\]
Area of a rectangle \[=\text{length}\times \text{breadth}\]


Complete Step by step solution:
\[\vartriangle \text{ACD}\] is a right angled triangle.
Using Pythagoras theorem formula;
\[\begin{gathered}
  & A{{C}^{2}}=A{{D}^{2}}+D{{C}^{2}} \\
 & A{{C}^{2}}={{5}^{2}}+{{12}^{2}} \\
 & A{{C}^{2}}=25+144 \\
 & A{{C}^{2}}=169 \\
 & AC=\sqrt{169} \\
 & AC=\pm \,13\text{ cm} \\
\end{gathered}\]
Since AC is a length it cannot be negative therefore AC= 13cm
Through AC which is the diameter of the circle, we can find the radius of the circle. from this circle, we will find the area of the circle.
Area of the shaded region \[=\] Area of the circle \[-\] area of the rectangle ABCD
Thus, by subtracting the area of the circle with the area of the inscribed rectangle we got the area of the shaded region.