The area of a shape is the amount of space it occupies.
The values of H and the length of the missing shorter base are: [tex]\mathbf{H = 8\ and\ B =2}[/tex]
The given parameters are:
[tex]\mathbf{Area = 40cm^2}[/tex]
[tex]\mathbf{Base_1 = 8cm}[/tex]
The area of a trapezoid is:
[tex]\mathbf{Area = \frac 12 \times (Base_1 + Base_2) \times Height}[/tex]
Substitute known values
[tex]\mathbf{40= \frac 12 \times (8 + Base_2) \times Height}[/tex]
Multiply through by 2
[tex]\mathbf{80= (8 + Base_2) \times Height}[/tex]
Make Height the subject
[tex]\mathbf{Height = \frac{80}{(8 + Base_2) }}[/tex]
Now, we make use of trial by error.
Let: [tex]\mathbf{Base_2 =1}[/tex]
So:
[tex]\mathbf{Height = \frac{80}{(8 + 1)} = \frac{80}{9} = 8.89}[/tex]
The above result is not a whole number.
Let: [tex]\mathbf{Base_2 =2}[/tex]
So:
[tex]\mathbf{Height = \frac{80}{(8 + 2)} = \frac{80}{10} = 8}[/tex]
The above result is a whole number.
So, the values of H and the length of the missing shorter base are:
[tex]\mathbf{H = 8\ and\ B =2}[/tex]
Read more about areas at:
https://brainly.com/question/15640807
