Question

lorea is designing the top of a quilt which measures 2,160 square inches. triangles will cover 432 square inches of the quilt, and squares will cover 180 square inches. the rest of the quilt will be parallelograms with a base of 2 inches and a height of 1.5 inches. how many parallelograms should she cut to complete the quilt?
○ 516
○ 528
○ 617
○ 720

Explanation:

Step1: Calculate the area covered by parallelograms

The total area of the quilt is \(2160\) square inches. The area covered by triangles is \(432\) square inches and by squares is \(180\) square inches.
The area for parallelograms \(A = 2160-(432 + 180)\)

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Step2: Calculate the area of one parallelogram

The formula for the area of a parallelogram is \(A_{p}=b\times h\), where \(b = 2\) inches and \(h=1.5\) inches.
\(A_{p}=2\times1.5=3\) square inches

Step3: Calculate the number of parallelograms

Let \(n\) be the number of parallelograms. Then \(n=\frac{\text{Total area for parallelograms}}{\text{Area of one parallelogram}}\)
\(n=\frac{1548}{3}=516\)

Answer:

A. 516