Question

Lucy’s rectangular garden is 15ft long and 12 ft wide. She adds a right triangle to her garden plan, so that the triangle’s height extends out 7ft in line with the shorter side of the rectangle, and the base of the triangle runs from the corner of the rectangle to the center of the longer side of the rectangle. Total area of Lucy’s garden:

Answer 1

Okay, so lets break this down.

First of all, we have the rectangular garden with a length of 15ft and a width of 12feet.  We need to find the area of this which is pretty simple.  This would be 15ft times 12ft which is 180ft².

Okay, now time for the triangle.  The way that it words it may be confusing but I can draw you a picture of what it looks like (its a quick draw so it looks kinda bad).

But, for the triangle we are going to extend the 12ft line (shorter side; width) and create a line that is 7 feet long.  Then, we are going to find the midpoint of the 15ft side and connect that with the end point of the triangle.

Since its on the longer side and its the midpoint, the triangle is going to have a base of 7.5ft (half of 15).  Then, the height is 7ft as included in the question.

Now to solve the area of a right triangle, you can use 1/2(bh).  So 1/2 of the base times height.

This is 1/2 of (7.5*7) which is 1/2(52.5) and finally the area of the triangle is 26.25ft².

Now, all you gotta do is add the 26.25ft² and the 180ft² together and you get 206.25ft²