Question

The measurement of a rectangle is 16 feet by 12 feet. What is the area of the smallest circle that can cover the rectangle entirely (so that no part of the rectangle is outside the circle)?

Answer 1

Answer:

diameter of the circle =sqroot of (16^2+12^2)=20feet

radius of the circle=20/2=10feet

area of the circle =(22/7)×10^2=/7=3.14×100=314sqfeet.

Answer 2

The area of the circle will be 314 square feet

Given:

Length of the rectangle = 12 feet

Breadth of the rectangle = 16 feet

To Find:

We need to find the area of the smallest circle that can enclose the given rectangle

Solution:

The smallest circle that can enclose a rectangle will have the radius of the circle as the diagonal of the rectangle.

This is depicted in the diagram given below.

Now, in triangle ABD, using Pythagoras theorem,

AB² + AD² = BD²

16² + 12² = BD²

256 + 144 = BD²

BD = √400

BD = 20

radius of the circle = 20/2 = 10

area of the circle = πr²

= 10²π

= 100 × 3.14

= 314

Thus, the area of the circle will be 314 square feet

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