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40 votes
40 votes
Work out the surface area of this solid

prism.
10cm
8cm
27cm
6cm
17cm
30cm
The diagram is not drawn to scale.

Work out the surface area of this solid prism. 10cm 8cm 27cm 6cm 17cm 30cm The diagram-example-1
User Rossi
by
3.0k points

1 Answer

11 votes
11 votes

Answer:

2064 cm²

Explanation:

You want the surface area of a prism that is 30 cm between bases that are trapezoids with parallel sides 27 cm and 6 cm that are 8 cm apart, and slant sides that are 10 cm and 17 cm.

Base area

The area of each trapezoidal base is ...

A = 1/2(b1 +b2)h

There are two identical bases, so their total area is ...

2A = (b1 +b2)h = (27 cm +6 cm)(8 cm) = 264 cm²

Lateral area

The lateral area of the prism is the area of the four rectangular faces. Each is 30 cm wide, and their total length is the perimeter of the base;

P = 27 cm +10 cm +6 cm +17 cm = 60 cm

lateral area = Ph = (60 cm)(30 cm) = 1800 cm²

Total surface area

The total surface area of the prism is the sum of the base area and the lateral area:

total area = base area + lateral area

total area = 264 cm² +1800 cm² = 2064 cm²

The surface area of the solid prism is 2064 cm².

User Weyhan
by
3.2k points
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