Quadrant area : ¼πr² or π × r × r ÷ 4

Taking π = 3.14, r = 10,

One quadrant's area

= ¼ × 3.14 × 10 × 10
= 78.5 cm²

Notice that the Square has a diagonal whose length is equal to the radius of the quadrant.

The diagonal divides it into two identical right-angled triangles with base 10 cm and height 5cm (try drawing the other diagonal to see the height)


So area of this square
= Area of two triangles
= ½ × 10 × 5 × 2
= ½ × 10 × 10
= 50 cm²

(You may also view it as 4 smaller right-angled triangles with base and height 5cm.

Area = 4 × ½ × 5 × 5 = 2 × 5 × 5 = 50 cm² )

Alternatively, the area of a square can also be said to be equal to:

½ d² or ½ × d × d

Where d is the length of its diagonal.

Next,

Unshaded area of one quadrant

= Quadrant area - square area
= 78.5 - 50
= 28.5 cm²

Total unshaded area
= Unshaded area of two quadrants
= 28.5 × 2
= 57 cm²

Many thanks