Can you help with Q12?
surface area question
surface area question
1 Answer
Explanation:
This one's a bit hard to type out.
First, I'll calculate the base. Assuming the bottom isn't included, each surface on the base is calculated with the classic formula,
We'll plug in the values for length and width,
Let's plug this into our handy calculator and get
But that's not all. Next, we calculate the surface area of the top. This is where is gets tricky.
The top is a pyramid, made up of four triangles. Each triangle base is
Now, imagine a dotted line falling from the very tip of the pyramid down to the middle of the base. This dotted line is now the leg of an imaginary right triangle. The length of this dotted line is
Still with me? It's hard to imagine without a picture.
By calculating the hypotenuse of this triangle, we get the slope of the entire pyramid. We'll use the Pythagorean theorem,
Plug that into your calculator and get
We'll leave it as that for now.
Now we have the slope of the pyramid, which is the height of the pyramid's triangle faces.
The area of a triangle is
There are four triangles, so we will multiple this by
Now, let's plug that into our calculator.
Our rounded answer is
To finish, we add both surface areas we found together.