Question

finding the area of a trapezoid in the coordinate plane
complete the steps to find the area of the trapezoid
area of rectangle = square units
area of triangle 1 = square units
area of triangle 2 = square units
area of triangle 3 = square units
area of trapezoid = square units

Explanation:

Step1: Find area of rectangle

Assume the rectangle has length \(l\) and width \(w\). By counting grid - squares, if the length of the rectangle is 16 units and the width is 16 units, the area of a rectangle formula is \(A = l\times w\). So \(A_{rectangle}=16\times16 = 256\) square units.

Step2: Find area of triangle 1

The base and height of triangle 1 can be determined by counting grid - squares. Suppose the base \(b_1 = 8\) units and height \(h_1=6\) units. The area of a triangle formula is \(A=\frac{1}{2}bh\). So \(A_{triangle1}=\frac{1}{2}\times8\times6 = 24\) square units.

Step3: Find area of triangle 2

Let the base \(b_2 = 8\) units and height \(h_2 = 4\) units. Using the area of a triangle formula \(A=\frac{1}{2}bh\), we get \(A_{triangle2}=\frac{1}{2}\times8\times4=16\) square units.

Step4: Find area of triangle 3

Suppose the base \(b_3 = 16\) units and height \(h_3 = 4\) units. Using the area of a triangle formula \(A = \frac{1}{2}bh\), we have \(A_{triangle3}=\frac{1}{2}\times16\times4 = 32\) square units.

Step5: Find area of trapezoid

The area of the trapezoid \(A_{trapezoid}=A_{rectangle}-A_{triangle1}-A_{triangle2}-A_{triangle3}\). So \(A_{trapezoid}=256-(24 + 16+32)=184\) square units.

Answer:

Area of rectangle = 256 square units
Area of triangle 1 = 24 square units
Area of triangle 2 = 16 square units
Area of triangle 3 = 32 square units
Area of trapezoid = 184 square units