Question

Please help ! Thank you in advance!!

Answer 1

Answer: $340cm^{2}$

Step-by-step explanation:

Ok, let's start easy by finding the area of the sides of this prism.

The sides of the prism are quite easy to find as they are just rectangles and the area of a rectangle is $A=lw$. The length is 10cm and the width is 5cm, so simply put the values into the formula and solve.

$A=(10)(5)$

$A=50$

So the area of a side is 50, but that's only 1 side; there are 5 sides in this prism so we must take the 50 and multiply it by 5 to find the area of all 5 sides combined, which would be 250.

Now the complicated part, the pentagon on the front and back.

Luckily, all the information is provided to us already.

The apothem is the length from the center of the pentagon to the 90 degree angle of the side, if that makes sense. So separate the pentagon into 5 triangles, then split those triangles down the center.

It should make 10 90 degree triangles, with the length from the edge to the center of the pentagon being 3.6cm and the base being 2.5cm as it is half the 5cm length of the pentagon side.

The area of a triangle is $A=\frac{1}{2}bh$

Simply plug in 3.6 for h and 2.5 for b and solve

$A=\frac{1}{2}(2.5)(3.6)$

$A=4.5$

The area is 4.5, but that's just 1/10th of the area of the pentagon, so we must multiply it by 10 to find the area of the entire pentagon, which is 45.

But, there is another pentagon in the back, so we must take 45 and multiply it by 2, getting 90.

Now that we have the area of the front and back pentagons, as well as the area of all the sides of the prism, all we need to do is add them all up together to find the total surface area.

$SA=250+90$

$SA=340$