Help 13

 

To do these problems we must first determine how many basic shapes we can fit in to the figure.  

 

Is see a rectangle and a triangle 

 

Now the we can simplify this by finiding the area of each indivdual shape let's start with the rectangle 

 

The formula for the rectangle is \(Length * With = Area\)or Vice Versa

 

so lets look for the with, on the bottom you can see that it's with is 11 cm 

 

Now we can plug that into our equation, so now we have \(11 * Length = Area\)

 

 

We still need to find the length so lets go back to arrow shape design...  If you look alont the side of only the rectangle you can see that it is equal 12 cm so we can plugh that value into our equation. \(11 * 12 = 132\) 

 

 

Now that we know that the area of the rectangle is exactly \(132{cm}^{2}\) 

 

The final thing left is only to find the area of the triangle 

 

and the formula for the area of a triangle is \(\frac{1}{2}* Base * Height = Area\) 

 

 

Now we know the base of the triangle form the figure shown is as wide as the shape will be so the base is equal to 13cm  

 

So we can plug that into our equation \(\frac{1}{2}* 13 * Height = Area\) 

 

NOW JUST THE HEIGHT!

 

 

 

Now it may look slightly difficult form not seeing a line cutting through the center for the triangle but we can see on the side of the entire figure 

 

that the entire shape is 15 cm long, remeber that rectangle well subtracting the length of the rectangle form the length of the entire figure will total 

 

in the height of the triangle so 15 - 12 = 3 

 

 

\(\frac{1}{2}* 13 * 3 = 19.5\) 

 

 

Now all we need to do is is add 19.5 and 132 so \(19.5 + 132 = 151.5 {cm}^{2}\) 

 

So our answer is 151.5 cm squared!