Charlie is re-landscaping his back yard and uses a coordinate plane to map the yard out. There is a pine tree located at (-5, 5); the edge of a shed is located at (-5, 1) and the edge of a sandbox is located at (2, 5). He plans to cover the triangular area formed by these three points with gravel. What area of the yard will be covered in gravel? Note: On the coordinate plane, each gridline represents 2 feet.

Accepted Solution

First I'd suggest plotting the points on a graph so that you can visualize the problem. What you're trying to find is the area of the triangle that the three points given will form. The area of a triangle is [tex] \frac{1}{2} bh[/tex] where b is the size of the base of the triangle and h is the height of the triangle. From graphing the three points and connecting them, you can see that the base of the right triangle formed is 4 units/gridlines and the height of the right triangle is 7 units/gridlines. SInce the problem specifies that each gridline is 2 feet, that means that the base 4 x 2 = 8 feet, and the height is 7 x 2 = 14 feet. Now you just plug these values into the equation for the area of a triangle to get [tex] \frac{1}{2} (8)(14)=56[/tex] feet squared as the area that will be covered in gravel.