Shape (higher)

Question 1

Find the area of this shape, giving your answer in terms of π.

Answer 1

0.75 × π × 8² =

48π

Question 2

What is the formula for the circumference of a circle?

Answer 2

Circumference

Question 3

What is the formula for the area of a circle?

Answer 3

Area of a circle

Question 4

What is the formula for the area of a trapezium?

Answer 4

Area of a trapezium

Question 5

What is the formula for the length of an arc?

Answer 5

Arc length =

Question 6

What is the formula for the area of a sector?

Answer 6

Sector area =

Question 7

Calculate the area of the shaded part, giving your answer in terms of π.

Answer 7

Area of the large circle minus the area of the small circle:

π × 5² – π × 2² = 25π – 4π = 19π

Question 8

Calculate the area and the perimeter of this trapezium.

Answer 8

Perimeter = 12 + 6 + 8.4 + 7 = 33.4cm

Area = (12 + 8.4) ÷ 2 × 6 = 61.2cm²

Question 9

Calculate the area of this compound shape

Answer 9

Area of the upper trapezium = (10 + 6) ÷ 2 × 4 = 32m²

Area of the lower trapezium = (10 + 3) ÷ 2 × 8 = 52m²

Total area = 32 + 52 = 84m²

Question 10

What percentage of this shape has been shaded?

Answer 10

Area of outer trapezium = (12 + 15) ÷ 2 × 9 = 121.5cm²

Area of inner triangle = 8 × 6 ÷ 2 = 24cm²

Shaded area = 121.5 – 24 = 97.5cm²

Percentage shaded = 97.5 ÷ 121.5 × 100 = 80.2% (1 dp)

Question 11

Calculate the perimeter of this shape

Answer 11

Arc length = 78 ÷ 360 × 12 × 2 × π = 16.34cm (2 dp)

Perimeter = 16.34 + 12 + 12 = 40.34cm

Question 12

Calculate the area of this sector

Answer 12

Sector angle = 360 – 120 = 240°

Sector area = 240 ÷ 360 × 3² × π = 18.85cm² (2 dp)

Question 13

Calculate the area of the shaded shape giving your answer in terms of π

Answer 13

Sector area = 90 ÷ 360 × 122 × π = 36πcm²

Triangle area = 12 × 12 ÷ 2 = 72cm²

Shaded area = (36π – 72)cm²