What’s the area of the shaded region? How could a landscaper know?
Let’s say you are a landscaper for a home builder and a particular layout of a house (white) and yard is given. The size of the lot changes but this is always the design. You need to be able to figure out how much yard you will work with on a house and give a quote of the amount you will charge the builder quickly.
First, put the numbers and variables to label the dimensions.
When solving a shaded region problem you want to find the area of the whole figure. Area of a rectangle is A = lw so the area of the entire lot is 3x(x + 5).
You then want to subtract the area of the house. This will leave the area of the yard which you will work with so your area problem becomes:
A = 3x(x + 5) − (x + 3)(x + 2)
As a landscaper, twice this month you punched in the wrong number, and it cost you money because you didn’t charge enough. You went back to the old method of measuring every single area and submitting your bid but it took too long and your competitor got the job.
Is there a way to simplify the expression so it is less likely you’ll make a mistake and still get your bid in quickly?
Simplify the algebraic expression 3x(x + 5) − (x + 3)(x + 2). Copy the problem in your notes. Complete each step until you have simplified the expression completely.
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