Question

Given two squares of the same length. One square has a triangle in it with its vertices coinciding with three vertices of the square. The other square contains a circle touching all mid points of the sides of the square.Which of these two will have a greater area and what is the difference in the areas if the length of the given square is 4m?
[4 MARKS]

Answer 1

Steps: 3 Marks
Answer: 1 Mark

The given square has a length of 4 m

Area of the Triangle = 0.5 $\times$ 4 $\times$ 4 = 8 $m^2$
The radius inscribed within the square has radius of $\frac{4}{2}=2m$
Area of the given circle = $\pi$ $\times$ $2^2$ =12.56 $m^2$
Circle has a greater area compared to triangle.
Difference between the area of the circle and triangle = 4.56 $m^2$