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5 of 6 Work out the surface area of this solid prism. 6cm 20cm 13cm 12cm 30cm 27 cm The diagram is not drawn to scale. cm2 book

User Danny Dan
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1 Answer

4 votes

The prism in the picture has 6 sides, three are shown.

We will have to calculate the area of each of them and sum.

The front and back surfaces are the same and are a trapezoid with height 12 cm, base 27cm and top 6cm.

We can use the area formula for trapezoid:


A=(\mleft(a+b\mright))/(2)h

Where, "a" and "b" are the base and top, and "h" is the height.

So:


A_(1,2)=(6+27)/(2)12=33\cdot6=198

So we have the area of the front surface 198 cm², since the back is the same we have two surfaces.

The top surface is a rectangle with dimensions 30 cm and 6cm, so its area is:


A_3=30\cdot6=180

It is 180 cm².

The surface at the right is also a rectangle with measures 30cm and 20cm, so:


A_4=30\cdot20=600

600 cm².

The surface of the left not appearing in the picure is also a rectangle and have measures 13cm and 30cm, so the area is:


A_5=30\cdot13=390

390 cm².

And the last is the bottom one, which is also a rectangle, with measures 27cm and 30cm.


A_6=30\cdot27=810

810 cm².

Now that we have all the areas,

User Logicalicy
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