Mr. Dennis is a farmer with two teenage sons. He gave them a rectangular piece of land with a creek running through it diagonally, as shown in the above figure. The elder boy took the larger area and the younger boy took the smaller. What is the area of each boy’s land in square feet?
To find the area of the smaller, triangular plot, use the formula for the area of a triangle, where A is the area, b is the base, and h is the height:
The whole piece of land is a rectangle, so you know that the corner the triangle shares with the rectangle is a right angle. Therefore, you know that the sides labeled 200 feet and 250 feet are the base and height. Find the area of this plot by plugging the base and height into the formula:
To make this calculation a little easier, notice that you can cancel a factor of 2 from the numerator and denominator:
The shape of the remaining area is a trapezoid. You can find its area by using the formula for a trapezoid, but there’s an easier way. Because you know the area of the triangular plot, you can use this word equation to find the area of the trapezoid:
Area of trapezoid = area of whole plot – area of triangle
To find the area of the whole plot, remember the formula for the area of a rectangle. Plug its length and width into the formula:
A = length width
A = 350 ft. 250 ft.
A = 87,500 square ft.
Now just substitute the numbers that you know into the word equation you set up:
So the area of the elder boy’s land is 62,500 square feet, and the area of the younger boy’s land is 25,000 square feet.