GCSE(F), GCSE(H),

A prism is a shape where the cross-sectional area remains the same throughout the length of the prism.

The surface area of a prism consists of the two ends, plus the surface area of the length.

Calculate the surface area of the two ends. Then work out the perimeter of one end, and multiply this perimeter by the length of the prism.

1. A right triangular prism (a triangular prism with a right angle) has sides of length 3cm, 4cm and 5cm. The prism is 15 cm long. What is the surface area of the prism?

Answer: 192 cm^{2}

The area of each trianglular end = `frac(1)(2)bh`

`A = frac(1)(2) xx 3 xx 4`

A_{triangle} = 6 cm^{2}

The perimeter of the triangle = 3 + 4 + 5 = 12 cm.

The surface area = surface area of both ends + surface area along length

A_{prism} = 2 x A_{triangle} + 12 x 15

A_{prism} = 2 x 6 + 12 x 15

A_{prism} = 12 + 180

A_{prism} = 192 cm^{2}

2. A prism is in the shape of a hexagon. The area of one end is 43.81 cm^{2}. The surface area of the entire prism is 500 cm^{2}. If the length of the prism is 40cm, what is the length, *x*, of one edge of the hexagon shape? Give your answer to 1 decimal place.

Answer: 1.7 cm

Surface area of prism = 2 x area of each end + length x perimeter

500 = 2 x 43.81 + 40 x p

412.38 = 40p

P = 10.3095

There are six sides to a hexagon

10.3095 รท 6 = 1.71 cm

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