Question

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

Answer 1

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,