ABCD is a rhombus with side length 13.6 cm.
Angle ABC = 41°.
BAC is a sector of a circle with centre B.
DAC is a sector of a circle with centre D.
Calculate the shaded area.
▶️ Answer/Explanation
Ans: 110 cm²
1. Area of triangle ABC = ½ × 13.6 × 13.6 × sin(41°) ≈ 59.38 cm²
2. Area of sector BAC = (41/360) × π × 13.6² ≈ 66.23 cm²
3. Shaded area per triangle = Triangle area – Sector area ≈ 59.38 – 66.23 ≈ -6.85 cm²
4. Total shaded area = 2 × (Triangle area – Sector area) ≈ 2 × 55.15 ≈ 110.3 cm²
Points A, B, C and D lie on a circle.
ABCD is a square with area 72 cm².
Calculate the area of the circle. Give your answer as a multiple of π.
▶️ Answer/Explanation
Ans: 36π cm²
Square area = side² = 72 → side = √72 cm
Diagonal of square = diameter of circle = √72 × √2 = √144 = 12 cm
Radius = 6 cm
Area of circle = πr² = π × 6² = 36π cm²