Sammy the school custodian is having a debate with Marci the museum curator. Sammy contends that the school is larger than the museum in terms of area. Marci contends the opposite.

To settle their debate, they find satellite images of both buildings and juxtapose them on a single coordinate grid (shown below).

The area of the school is

\text{m}^2m

2

start text, m, end text, squared.

Round the final answer to the nearest square meter. Do not round intermediate calculations.

The area of the museum is

\text{m}^2m

2

start text, m, end text, squared.

Round the final answer to the nearest square meter. Do not round intermediate calculations.

Who should win the debate?

Choose 1 answer:

Choose 1 answer:

(Choice A)

A

Sammy

(Choice B)

B

Marci

It is convenient to compute the areas in terms of grid squares. Then those results can be converted to square meters by multiplying by the area of a grid square: (10 m)² = 100 m².

(a) The area of the school is the product of its side dimensions. The short side is (in terms of grid squares) ...

W = √(1²+3²) = √10

The long side is ...

L = √(2²+6²) = √40

Then the area is ...

A = LW = (√40)(√10) = √400 = 20

The area of the school is 20 grid squares = 2000 m² . . . . . where s = 10 m

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(b) The area of the museum is given by the formula ...

A = πr² = π(3)² = 9π grid squares = 2827 m²

The area of the museum is 2827 m².

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(c) Marci says the museum has a larger area than the school. She is correct.

Marci should win the debate.