Question

what is the area of this parallelogram? 56 square inches 105 square inches 150 square inches 255 square inches

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 7\) inches and \(w=8\) inches. So, \(A_{rectangle}=7\times8 = 56\) square inches.

Step2: Calculate the area of one triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\). Here, \(b = 7\) inches and \(h = 7\) inches. So, \(A_{triangle}=\frac{1}{2}\times7\times7=\frac{49}{2}=24.5\) square inches.

Step3: Calculate the area of two triangles

Since there are two congruent triangles, \(A_{two - triangles}=2\times24.5 = 49\) square inches.

Step4: Calculate the area of the parallelogram

The area of the parallelogram \(A = A_{rectangle}+A_{two - triangles}\). Substitute the values: \(A=56 + 49=105\) square inches.

Answer:

105 square inches