Answer:
To find the volume of this figure, we must find the base area(pentagon) and multiply it by the figure's height.
Formula for area of a pentagon:-
A = 1/2 x p x a
Where 'p' represents the perimeter, and 'a' represents the apothem.
First, let's figure out the perimeter of the base pentagon.
One side of this pentagon is 10cm, and there are 5 side lengths of 10cm to this pentagon. So it'll result in (5 x 10) = <u>50cm</u> altogether.
The apothem is given, <u>6.9cm</u>.
So, we plug these into our formula:-
A = 1/2 x p x a
A = 1/2 x 50 x 6.9
A = 50/2 x 6.9
A = 25 x 6.9
A = <u>172.5cm</u>, is the area of the pentagon.
Now we find the height of this figure and multiply it by the base area we've found(pentagon).
Our height is 17cm.
172.5(17)
= <u>2,932.5 cubic centimetres</u>, is our volume.
