Question

find the area of the figure below by first finding the areas of the rectangle and triangle. area of the rectangle: square units area of the triangle: square units area of the figure: square units

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). From the figure, assume the length \(l = 3\) units and the width \(w=2\) units. Then \(A_{rectangle}=3\times2 = 6\) square units.

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\). Assume the base \(b = 3\) units and the height \(h = 3\) units. Then \(A_{triangle}=\frac{1}{2}\times3\times3=\frac{9}{2}=4.5\) square units.

Step3: Calculate the area of the figure

The area of the figure is the sum of the area of the rectangle and the area of the triangle. So \(A = A_{rectangle}+A_{triangle}=6 + 4.5=10.5\) square units.

Answer:

Area of the rectangle: \(6\) square units
Area of the triangle: \(4.5\) square units
Area of the figure: \(10.5\) square units