Question

Cameron is designing a table for his game room. Cameron decides to make the center part of the tabletop out of inlaid wood. He sketches the design shown, where four trapezoids form a square with 6-inch sides in the middle of the table. What is the length, d, of the side of each trapezoid? Round to the nearest tenth of an inch. Explain.

I NEED THIS SOLVED QUICKLY WITH AND EXPLAINATION AND WORK SHOWN HURRY

Answer 1

d = 12.7 inches

Explanation:

First we convert 2 feet to inches:

2 feet = 2*12 inches = 24 inches.

If we project the side of the central square to the side of the bigger square, we will have two points in the side of the bigger square, dividing it in three parts, that measures:

x, 6 in, x

Where x = (24 - 6) /2 = 9 inches

As the figure is simetrical, the height of each trapezoid is also x, as we can do the same procedure above for the 4 trapezoids.

Then, we will have a small right rectangle, with sides of length x and hypotenusa d, so we can find d using Pythagoras' theorem:

d^2 = 9^2 + 9^2

d^2 = 162

d = 12.728 inches

Rounding to nearest tenth, we have d = 12.7 inches