Question

In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is​

Answer 1

GIven: ABCD is square with side 14 cm and E,F,G,H are the midpoints of the sides of the square.

To find the area of the shaded region.

Solution:

Observe the given figure.

The given square is divided into two parts one of the parts has a half square and a semicircle and the other part has the other of the square and two quadrants which is equal to a semicircle.

Find the area of the shaded portion.

Shaded area = Area of semicircle + (Area of half square – Area of two

                                                                                                    quadrants)

$\[ \Rightarrow \]$Shaded area = Area of semicircle +(Area of half square – Area of

                                                                                                       semicircle)

$\[ \Rightarrow \]$Shaded area= Area of half square

                        $\[\begin{array}{l} = \frac{1}{2} \times 14 \times 14\\ = 14 \times 7\\ = 98 cm^{2} \end{array}\]$

Hence, the area of the shaded portion is $98 cm^{2}$.