Question

How many square feet of out door carpet will we need for this hole

Answer 1

Hey! Let me help you on this one.

As you can see, this is a very complex shape, and this might confuse you at first. Don't fear, there is a very easy and fun way to solve it.

Take a closer look at the problem. Do you notice anything? It consists of few different shapes that might be much easier for you to find area of. 

For example, as you can see on the image I have sent you, these are the shapes present in the figure.

On this image, only two types of figures are present - triangle and a rectangle. Both shapes have a very easy area formula.

Triangle - $S= \frac{a*b}{2}$

Rectangle - $S=a*b$

Using these formulas, let's find the area of this complex figure by solving for each individual shape, and then, adding everything together.

Triangle at the bottom has a side of 4 feet, and an unknown second side. We can find it by getting the difference of 12 feet and 8 feet.

Why you might ask? Well, if you look at it closer, the difference is exactly the length of the side we need.

$12-8=4$

Neat! It's four as well. Let's start solving for its area.

$S= \frac{4*4}{2}$
$S=8$

Area of the first triangle is 8 feet squared. Let's get into the second triangle. It's right above this one!

Length of its right side is 3 feet, and the length of the bottom side is the same as the one we found few steps back - four feet.

$S= \frac{4*3}{2}$
$S= 6$

Awesome! Area of the second triangle is 6 feet squared. Let's take a closer look at the last figure - rectangle.

$S=8*3$
$S=24$

Area of the rectangle is 24 feet squared. Done, we have all the areas of individual shapes. Let's add them together.

$24+6+8=38$

Answer: The area of this figure is 38 feet squared