Question

distance between grid lines is 3 feet. alan wants to install security cameras in his store, which has dimensions of 30 feet by 30 feet. each camera can view an area of approximately 112.5 ft², with a viewing area shaped like a right triangle. how many cameras will be necessary to cover the entire store? if he places cameras only in the corners of the store, how much area is left uncovered? ft² 112.5 225 337.5 450

Explanation:

Step1: Calculate the area of the store

The store has dimensions of \(30\) feet by \(30\) feet. Using the formula for the area of a rectangle \(A = l\times w\), we have \(A_{store}=30\times30 = 900\ ft^{2}\).

Step2: Calculate the number of cameras

Each camera covers an area of \(A_{camera}=112.5\ ft^{2}\). The number of cameras \(n=\frac{A_{store}}{A_{camera}}\). So \(n=\frac{900}{112.5}=8\).

Step3: Calculate the uncovered area when cameras are placed in corners

If we place cameras in the corners (assuming 4 cameras, but since the area of each camera is \(112.5\ ft^{2}\), and if we consider the total covered area by 4 cameras \(A_{covered}=4\times112.5 = 450\ ft^{2}\). The uncovered area \(A_{uncovered}=A_{store}-A_{covered}\). So \(A_{uncovered}=900 - 450=450\ ft^{2}\)

Answer:

The number of cameras is \(8\). The uncovered area is \(450\ ft^{2}\)