Mathematics - Shapes (Area & Perimiter GCSE) Sorry I tried to attach photo but it wouldn't load so link below Photo : https://ibb.co/e1FT6G?

a) The perimeter of the leaf is half the crcumference of a circle of radius 20 cm, hence

.. (1/2)*(2π(20 cm) = 20π cm

b) The area of the leaf is the area of a semicircle of radius 20 cm less the area of a square 20 cm on a side.*

.. (1/2)π(20 cm)^2 -(20 cm)^2 = (200π -400) cm^2 = 200(π -2) cm^2

___

* Draw a diagonal line between the vertices of the leaf. The area below the line is half the area of a 20 cm square. The area above the line is half the area of the leaf. The area in the square below the upper curve is 1/4 of the circle. The whole leaf area will be 2*(1/4 circle -1/2 square) = 1/2 circle -1 square.

Presumably the arc centers are corners of the square. If so each arc is 90° so total arc length is half circumference of a circle of radius 20, which is (2πr) / 2 = πr with r=20, so 20π.

The area of one purple corner is squares area minus area of one quarter circle, which is

20^2 - πr^2/4 with r=20, which is 20^2 (1-π/4), double that and subtract from area of square to get leaf's area, namely 20^2 - 20^2 (2-π/2) = 20^2 (1 - 2 + π/2) = 400(π/2 - 1) = 200(π - 2).

The leaf consists of the intersection of 2 quarter circles of radius 20 cm

a.

Circumference of each circle = 2πr = 40π cm

P = 2 * 1/4 * (40π cm) = 20π cm

b.

Area of each circle = πr² = 400π cm²

Area of square = (20 cm)² = 400 cm²

Each corner has area = Area of square − Area of 1/4 circle

= 400 cm² − 1/4 (400π cm²) = (400−100π) cm²

Area of leaf = Area of square - Area of both corners

= 400 cm² − 2 (400−100π) cm²

= (200π − 400) cm²

= 200(π−2) cm²

Formulas:

Arc length = r(x) ,

Sector area = (1/2)(x)(r^2) , where r=radius , x=center angle in radians