A rectangular backyard is 30 feet long and 20 feet wide. A... | SAT Area and volume Question, Answer Explained

Math · Geometry and TrigonometryEasy

A rectangular backyard is $30$ feet long and $20$ feet wide. A square patio with a side length of $8$ feet is built in the backyard. What is the area, in square feet, of the part of the backyard not covered by the patio?

$536$

$568$

$584$

$664$

Show answer and explanation

Answer: A

The area of the backyard is $30 \times 20 = 600$ square feet. The area of the patio is $8^2 = 64$ square feet. The area not covered is $600 - 64 = 536$ square feet.

Choice B subtracts the patio's perimeter, $4 \times 8 = 32$ , instead of its area.

Why the other choices are wrong

B. This subtracts the patio's perimeter, 32, instead of its area, 64.
C. This subtracts 8 × 2 = 16 instead of 8 squared.
D. This adds the patio's area instead of subtracting it.

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