Question

understanding the area formula
look at the drawing of a triangle within a rectangle. the triangle and the rectangle have the same base, b, and height, h.
if the area of the triangle is 48 square units, what is the total area of sections 1 and 2?
square units

Explanation:

Step1: Recall the area formulas

The area of a rectangle is \(A_{rectangle}=b\times h\), and the area of a triangle is \(A_{triangle}=\frac{1}{2}\times b\times h\).

Step2: Relate the areas

We know that \(A_{triangle} = 48=\frac{1}{2}\times b\times h\). Then \(b\times h=48\times2 = 96\) (since \(A_{rectangle}=b\times h\) and \(A_{triangle}=\frac{1}{2}\times A_{rectangle}\)).

Step3: Find the area of sections 1 and 2

The sum of the areas of sections 1 and 2 is \(A_{rectangle}-A_{triangle}\). Since \(A_{rectangle}=96\) and \(A_{triangle} = 48\), then \(A_{1 + 2}=96 - 48=48\).

Answer:

48