High School

The diagram shows a prism.

The cross section of the prism is a right-angled triangle.

The lengths of the sides of the triangle are 8 cm, 15 cm and 17 cm.

The length of the prism is 20 cm.

Work out the total surface area of the prism.

Diagram NOT

accurately drawn

8 cm

17 cm

20 cm

15 cm

The diagram shows a prism The cross section of the prism is a right angled triangle The lengths of the sides of the triangle are

Answer :

Answer:

Total surface area of the prism = 920 cm²

Step-by-step explanation:

Given prism has 2 similar triangular surfaces and 3 rectangular surfaces of different dimensions.

Area of one triangular side = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

Area of 2 similar sides = Base × Height

= 8 × 15

= 120 cm²

Area of rectangular side with dimensions 17cm × 20cm

Area of the side = 17 × 20 = 340 cm²

Area of the second rectangular side with dimensions 8cm × 20cm

Area of the side = 8 × 20 = 160 cm²

Area of third rectangular side with dimensions 20cm × 15cm

Area of the side = 20 × 15 = 300 cm²

Total surface area of the given triangular prism = 120 + 340 + 160 + 300

= 920 cm²