Question

Mariah's house sits on an irregular lot with a triangular-shaped backyard. Most of the backyard will be grass, but Mariah would also like a rectangular garden plot. Before she heads to the garden center, she needs to calculate a few measurements. How many square yards will be grass?
24 yd 2
46 yd 2
22 yd 2
18 yd 2

Answer 1

For this, you'll be subtracting the area of the garden plot from the area of the whole backyard. However, you need to convert feet to yards. I'll be using dimensional analysis to solve that:

$\frac{2 ft}{1} *\frac{12in}{1ft} *\frac{1yd}{36in} =\frac{24}{36} =\frac{2}{3} yd$

Now that we know its 2/3 yd, we can solve for the areas.

Rectangle: $A=bh \\A=\frac{3}{1} *\frac{2}{3} \\ \\ A=\frac{6}{3} =2$

Triangle: $A=\frac{1}{2} bh\\ \\A=\frac{1}{2} *6*8\\\\ A=24$

Now that we got the areas, its time to subtract: $24-2=22$

The grass will be 22 yds^2