Area of the rectangle: 112
Step-by-step explanation:
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The area of a triangle is given by
[tex]A=\frac{1}{2}bh[/tex]
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:
[tex]AE=b=\frac{2A}{h}=\frac{2(40)}{8}=10[/tex]
Now we observe that the base of the rectangle, AD, is the sum of AE and DE, therefore:
[tex]AD=AE+DE=10+4=14[/tex]
We also know the height of the rectangle AB is 8, and that the area of a rectangle is
[tex]A=bh[/tex]
where b is the base and h the height. Therefore, the area of this rectangle is
[tex]A=bh=(AD)(AB)=(14)(8)=112[/tex]
Learn more about area of figures:
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