Question

a developer buys an empty lot to build a small house. what is the area of the lot?

Explanation:

Step1: Divide the lot into two triangles

The lot can be divided into two triangles. One triangle has vertices \((0,10)\), \((- 8,0)\), \((0,0)\) and the other has vertices \((0,10)\), \((0,0)\), \((8,0)\).

Step2: Calculate the area of the first triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). For the first triangle with base \(b = 8\) (distance from \((-8,0)\) to \((0,0)\)) and height \(h = 10\) (distance from \((0,0)\) to \((0,10)\)), \(A_1=\frac{1}{2}\times8\times10 = 40\).

Step3: Calculate the area of the second triangle

For the second triangle with base \(b = 8\) (distance from \((0,0)\) to \((8,0)\)) and height \(h = 10\) (distance from \((0,0)\) to \((0,10)\)), \(A_2=\frac{1}{2}\times8\times10=40\).

Step4: Calculate the total area

The total area \(A = A_1+A_2\). So \(A=40 + 40=80\).

Answer:

\(80\) square yards