Question

in building a house, sabrina wants to know how much water will run off of the roof in a heavy rainstorm. the first step in figuring this out is to calculate the area of the plane of the roof. if the corners of the roof are at the locations shown, what is the area of the roofs plane? first find the unknown segment length(s), then calculate the area of the polygon. area of the rectangle: square feet

Explanation:

Step1: Identify the length and width of the rectangle

The points \(G(0,49)\) and \(Q(29,49)\) give the length along the x - axis. The length \(l\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) with \(y_1 = y_2\) is \(|x_2 - x_1|\). Here, \(l=|29 - 0|=29\). The points \(Q(29,49)\) and \(W(29,- 1)\) give the width along the y - axis. The width \(w\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) with \(x_1 = x_2\) is \(|y_2 - y_1|\). Here, \(w=|49-(-1)| = 50\).

Step2: Calculate the area of the rectangle

The area formula of a rectangle is \(A=l\times w\). Substitute \(l = 29\) and \(w = 50\) into the formula. So \(A=29\times50=1450\).

Answer:

1450