Area of the rectangle: 112
Step-by-step explanation:
Picture is missing: find it in attachment.
The area of a triangle is given by
![A=\frac{1}{2}bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dbh)
where
b is the length of the base
h is the height
For triangle ABE, we know that
A = 40 (area)
h = 8 (height)
So we can find the length of the base AE:
![AE=b=\frac{2A}{h}=\frac{2(40)}{8}=10](https://tex.z-dn.net/?f=AE%3Db%3D%5Cfrac%7B2A%7D%7Bh%7D%3D%5Cfrac%7B2%2840%29%7D%7B8%7D%3D10)
Now we observe that the base of the rectangle, AD, is the sum of AE and DE, therefore:
![AD=AE+DE=10+4=14](https://tex.z-dn.net/?f=AD%3DAE%2BDE%3D10%2B4%3D14)
We also know the height of the rectangle AB is 8, and that the area of a rectangle is
![A=bh](https://tex.z-dn.net/?f=A%3Dbh)
where b is the base and h the height. Therefore, the area of this rectangle is
![A=bh=(AD)(AB)=(14)(8)=112](https://tex.z-dn.net/?f=A%3Dbh%3D%28AD%29%28AB%29%3D%2814%29%288%29%3D112)
Learn more about area of figures:
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