Class X

Area of a Circle I

Lesson

We already know that area is the space inside a 2D shape. We can find the area of a circle, but we will need a special rule.

The following investigation will demonstrate what happens when we unravel segments of a circle.

Created with Geogebra

Interesting isn't it that when we realign the segments we end up with a parallelogram shape. Which is great, because it means we know how to find the area based on our knowledge that the area of a parallelogram has formula $A=bh$A=bh. In a circle, the base is half the circumference and the height is the radius.

Area of a Circle

$\text{Area of a circle}=\pi r^2$Area of a circle=πr2

Worked Examples

QUESTION 1

If the radius of the circle is $5$5 cm, find its area.

Give your answer as an exact value.

QUESTION 2

Find the area of the shaded region in the following figure, correct to one decimal place.

QUESTION 3

Find the area of the shaded region in the following figure, correct to one decimal place.

A figure of a square with a quarter-circle cut out of it such that the bottom-right corner of the square intersects with the corner of the quarter-circle. The bottom-right corner has a small square indicating a right angle. The top and left sides of the square each has a tick mark. The right side of the square is divided into two segments with $4$4-cm segment on top of the $20$20-cm segment. The $20$20-cm segment is also the radius of the quarter-circle.

Outcomes

10.M.AC.1

Area of a circle, sectors and segments. Problems based on areas and perimeter/circumference of the above said plane figures. Restrict to central angles of 60, 90 and 120 degrees and plain figures of triangles, simple quadrilaterals and circles.