Question

What is the area of the shaded part?

Answer 1

Your answer would be 44in².

To find the area of the shaded part, we need to find the area of the whole triangle and then subtract the area of the small rectangle.

The equation for the area of a triangle is (base × height)/2, so in the triangle we’re given we can deduce that the total height is 8 inches, as it’s the 5 inches already shown in the triangle plus the height of the rectangle. We can also deduce that the base of the triangle is 14 inches long, because we end up with 5 + 5 + 4 = 14.

This gives us the area of the triangle as (14 × 8)/2 = 112/2 = 56 in².

Now we just need to find the area of the rectangle which is simply base × height. This gives us 4 × 3 = 12 in².

Our final answer is therefore 56 - 12 = 44 in².

I hope this helps!