Question

the coordinate plane shows parallelogram abcd. what is the area of the parallelogram? enter your answer in the box. square units

Explanation:

Step1: Find the area of the rectangle

Assume the rectangle that encloses the parallelogram has length \(l = 7\) units and width \(w=9\) units.
The area of the rectangle \(A_{rectangle}=l\times w = 7\times9=63\) square units.

Step2: Subtract the areas of the four right - angled triangles

• Triangle 1: base \(b_1 = 2\), height \(h_1=5\), area \(A_1=\frac{1}{2}\times2\times5 = 5\)
• Triangle 2: base \(b_2 = 2\), height \(h_2=4\), area \(A_2=\frac{1}{2}\times2\times4 = 4\)
• Triangle 3: base \(b_3 = 5\), height \(h_3=2\), area \(A_3=\frac{1}{2}\times5\times2 = 5\)
• Triangle 4: base \(b_4 = 4\), height \(h_4=2\), area \(A_4=\frac{1}{2}\times4\times2 = 4\)

The sum of the areas of the four triangles \(A_{triangles}=A_1 + A_2+A_3+A_4=5 + 4+5+4=18\)

Step3: Calculate the area of the parallelogram

The area of the parallelogram \(A = A_{rectangle}-A_{triangles}\)
\(A=63 - 18=35\)

Answer:

35