The area of a shape is the amount of space it can occupy.
Laura's design will be light enough
The shape is given as a trapezium (see attachment).
First, calculate the height (h) of the trapezium using the following Pythagoras theorem
[tex]5^2 = h^2 + x^2[/tex]
Where:
[tex]x = \frac{11 - 9}{2} = 1[/tex]
So, we have:
[tex]5^2 = h^2 + x^2[/tex]
[tex]5^2 = h^2 + 1^2[/tex]
[tex]25 = h^2 + 1[/tex]
Collect like terms
[tex]h^2 = 25 -1[/tex]
[tex]h^2 = 24[/tex]
Take square roots
[tex]h = 4.90[/tex]
The area of the shape is then calculated as follows:
[tex]Area = \frac{1}{2}(11 + 9) \times h[/tex]
[tex]Area = \frac{1}{2}(11 + 9) \times 4.90[/tex]
[tex]Area = \frac{1}{2} \times 20 \times 4.90[/tex]
[tex]Area = 10 \times 4.90[/tex]
[tex]Area = 49[/tex]
The area of the shape is 49 square inches.
Hence, the shape will be light enough (because 49 is less than 80)
Read more about areas at:
https://brainly.com/question/16418397
