Question

7 a baseball diamond has an area of 3,600 ft². what is the distance between each base? how far does a runner run around the bases when hitting a home run? 8 a postcard in the shape of a parallelogram has an area of 12 in.². what are two possible lengths of bases and heights for the postcard?

Explanation:

Step1: Find the distance between each base (side length of the square)

A baseball diamond is a square. The area formula for a square is \(A = s^{2}\), where \(s\) is the side - length. Given \(A=3600\space ft^{2}\), then \(s=\sqrt{A}\).

$$s = \sqrt{3600}=60\space ft$$

Step2: Find the distance a runner runs (perimeter of the square)

The perimeter formula for a square is \(P = 4s\). Since \(s = 60\space ft\), then \(P=4\times60\).

$$P=240\space ft$$

Step3: Find possible base and height for the parallelogram

The area formula for a parallelogram is \(A = bh\), where \(b\) is the base and \(h\) is the height. Given \(A = 12\space in^{2}\).
If \(b = 3\space in\), then \(h=\frac{A}{b}=\frac{12}{3}=4\space in\).
If \(b = 2\space in\), then \(h=\frac{A}{b}=\frac{12}{2}=6\space in\)

Answer:

• Distance between each base: \(60\space ft\)
• Distance a runner runs: \(240\space ft\)
• Two possible base - height pairs for the parallelogram: \((b = 3\space in,h = 4\space in)\) and \((b = 2\space in,h = 6\space in)\)