Question

10.
B
In the given figure, AB = 8 cm; BC = 12 cm; AE = 6 cm then find the area
of rectangle BCDE. B
A
E
D​

Answer 1

Answer:

Step 1:

It is given,

AB = length of the rectangle = 8 cm

BC = breadth of the rectangle = 6 cm

From the figure attached below we can see that AC is the diagonal of the rectangle, therefore, by using the Pythagoras theorem, we get

AC = √[AB² + BC²] = √[8² + 5²] = √[100] = 10 cm

Also, AC is the diameter for the circle that inscribes the rectangle.

∴ Radius of the circle = \frac{AC}{2}

2

AC

= \frac{10}{2}

2

10

= 5 cm

Step 2:

Area of the rectangle = length * breadth = 8 * 6 = 48 cm²

And,

Area of the circle = πr² = (22/7) * 5² = 78.57 cm²

Thus,

The area of the shaded region is given by,

= [Area of the circle] – [Area of the rectangle]

= 78.57 cm² - 48 cm²

= 30.57 cm²