Area of Triangle inside Rectangle

Question

A rectangle has an area of 72in². The lines from the top left intersects the right side and bottom side at half their lengths to form a triangle inside the resctangle. What is the area of the inside triangle?

Answer 1

Well, I wish I could draw a picture for you to explain how I got my answer. I'll try and describe it.

 

When you draw a segment from the corner of a rectangle to the midpoint of a side, the triangle formed is always 1/4 of the total area of the rectangle. The area of the rectangle is l*w. the area of the triangle is 1/2 (1/2l)*w or 1/2 (1/2w)*l. in either case, the resulting triangle is 1/4 l*w which is 1/4 of the area of the rectangle. 

 

Since you have two triangles ike this, that represents 1/2 of the rectangle.

 

The bottom, little triangle in the lower right hand corner is A=1/2*(1/2w)*( 1/2l) = 1/8 l*w or 1/8 the area of the rectangle.

 

We can now subtract each of these from the entire rectangle to get Area of your triangle = L*W-1/2L*W-1/8L*W which is the same as A=3/8 L*W. So your triangle has the area 3/8*72 = 27 sq. in.

 

Hope this helped.