Question

find the area of each part of the figure and the whole figure.
figure area (square units)
rectangle a
triangle b
whole figure

Explanation:

Step1: Calculate the area of Rectangle A

The formula for the area of a rectangle is \(A = l\times w\). For rectangle A, \(l = 9\) and \(w = 5\).
\(A_{A}=9\times5 = 45\)

Step2: Calculate the area of Triangle B

First, find the base of the triangle. The vertical side of the whole figure is \(13\), and the height of rectangle A is \(9\), so the height of the triangle \(h=13 - 9=4\). The base of the triangle \(b = 5\). The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\).
\(A_{B}=\frac{1}{2}\times5\times4=\frac{1}{2}\times20 = 10\)

Step3: Calculate the area of the whole figure

The area of the whole figure \(A_{total}=A_{A}+A_{B}\)
\(A_{total}=45 + 10=55\)

Answer:

Rectangle A: \(45\), Triangle B: \(10\), Whole figure: \(55\)