The area of a shape is the amount of space the shape can occupy.
The values of the height and the shorter base are: 8cm and 2cm respectively
The given dimensions are:
[tex]\mathbf{Area = 40cm^2}[/tex]
[tex]\mathbf{Base = 8cm}[/tex]
The area of a trapezoid (see attachment) is:
[tex]\mathbf{Area = \frac 12(Base_1 + Base_2) \times Height}[/tex]
So, we have:
[tex]\mathbf{40 = \frac 12(8 + Base_2) \times Height}[/tex]
Multiply through by 2
[tex]\mathbf{80 = (8 + Base_2) \times Height}[/tex]
The whole number values of base and height that satisfy the above equation is:
[tex]\mathbf{Base_2 = 2}[/tex]
[tex]\mathbf{Height = 8}[/tex]
i.e.
[tex]\mathbf{80 = (8 + Base_2) \times Height}[/tex]
[tex]\mathbf{80 = (8 + 2) \times 8}[/tex]
[tex]\mathbf{80 = 10 \times 8}[/tex]
[tex]\mathbf{80 = 80}[/tex]
Hence, the values of the height and the shorter base are: 8cm and 2cm respectively
Read more about areas at:
https://brainly.com/question/16418397
