Shape and Space 7

3 marks · Easy

The two pentagons below are similar. The side of the smaller pentagon is 4 cm. The side of the larger pentagon is 10 cm.

(a)

Write down the scale factor for the sides from the smaller pentagon to the larger pentagon.

[1 mark]

(b)

If the area of the smaller pentagon is 13 cm², calculate the area of the larger pentagon.

[2 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) 2.5

(b) 81.25 cm^2

Common mistakes: Uses incorrect power for area scale factor.; Multiplies area by side scale factor instead of its square.; Divides instead of multiplies.

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Writes correct scale factor for sides (10/4 = 2.5 or equivalent fraction).

M1 (b) · 1 mark · Squares the scale factor to get the area scale factor.

A1 (b) · 1 mark · Correctly calculates larger pentagon's area as 81.25 cm². (follow-through)

Worked solution

a) Scale factor =

b) Area scale factor =

Area of larger pentagon = cm²