Draw the diagonal of the square. It is now divided into 2 identical right angled isosceles triangles.

area of unshaded half-leaf = area of big quarter circle - area of triangle

= (π x 20 x 20 x ¼ - ½ x 20 x 20) cm²
= (100π - 200) cm²

Area of unshaded leaf

2 x (100π - 200) cm²
= (200π - 400) cm²



Area of square = 20cm x 20cm = 400 cm²
Area of circle = π x 10cm x 10cm = 100π cm²

Area of 4 corners = (400 - 100π) cm²
Area of 2 corners = ½ x (400 - 100π)cm²
= (200 - 50π)cm²


Area of shaded parts

= Area of square - area of 2 corners - area of unshaded leaf

= 400cm² - (200 - 50π)cm² - (200π - 400)cm²

= 400 cm² - 200 cm² + 50π cm² - 200π cm² + 400cm²

= 600cm² - 150π cm²

≈ 128.76 cm² (using calculator value of π)
= 128.8 cm² (1 d.p)

You shouldn't be using 3.14 in this question

Another way :


Area of one large corner

= Area of square - area of big quarter circle
= 20 cm x 20 cm - ¼ x π x 20 cm x 20 cm
= 400 cm² - 100π cm²

≈ 85.84 cm² (2 d.p)


Area of one small corner

= ¼ (area of square - area of circle)
= ¼ (400 cm² - π x 10 cm x 10 cm)
= ¼ (400 cm² - 100π cm²)
= 100 cm² - 25π cm²

≈ 21.46 cm² (2.dp)


Area of 1 shaded part

= Area of one large corner - area of one small corner

= 85.84 cm² - 21.46 cm²
= 64.38 cm²

Area of 2 shaded parts

= 64.38 cm² x 2
= 128.76 cm²

= 128.8 cm² (1 d.p)