Question

What is the area of this

Answer 1

The figure has already been split into 3 shapes, a rectangle, a trapezium, and a triangle. I will show you how to get the area of each, so we can add it together at the end.

Rectangle:
The rectangle is fairly simple, just multiply 9 and 16 together to get 144 in².

Triangle:
Again, the triangle is pretty simple. The area of a triangle is (base × height)/2, so you do (31 × 20)/2 = 620/2 = 310 in².

Trapezium:
To find the area of a trapezium, you first add the two widths, which are 16 and 31, and then you divide it by 2. You then multiply that value by the height. 16 + 31 = 47, and 47 ÷ 2 = 23.5.
The height would be 35 (the total length of the shape) - 20 (the height of the triangle) which is 15, so 23.5 × 15 = 352.5 in².

Now we add them up, so 144 + 310 + 352.5 = 806.5 in², which is your final answer.

I hope this helps!