Question

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?

Answer 1

(Satellite images of both the buildings on a single coordinate grid are shown in the ATTACHMENT)

MARCI SHOULD WIN

AREA OF MUSEUM > AREA OF SCHOOL

Explanation:

Find the area of School in Grid squares:

`Width=√(1^2+3^2)\\ Width=√(10)\\Length=√(2^2+6^2)\\Length=√(40)\\Area=(Length)\cdot(Width)=√(40)√(10)=20\\`

Area of School = 20 Grid squares*10*10

Area of School = 2000 m²

Find the area of Museum in Grid squares:

`A=\pi{r^2}\\A=\pi(3^2)\\A=9\pi`

Area of Museum = 9п grid squares

Area of Museum = 2826 m²

AREA OF MUSEUM > AREA OF SCHOOL