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A grid 16 columns by 8 rows shows a trapezoid on it. The top left vertex is at the start of 2nd row and end of 3rd column. The top right vertex is at the start of 2nd row and end of 13th column. The bottom left vertex is at the end of 7th row and end of 1st column. The bottom right vertex is at the end of 7th row and end of 15th column.

A designer wants to estimate the area of a trapezoid-shaped stage. Each square represents one square foot. The designer decides to find the area of the stage by composing a rectangle. What is the length of the base of the newly composed rectangle in feet?

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1 answer

To find the length of the base of the newly composed rectangle for the trapezoid, we need to determine the length of the bottom base of the trapezoid.

The coordinates of the vertices are:

  • The top left vertex is at (3, 2)
  • The top right vertex is at (13, 2)
  • The bottom left vertex is at (1, 7)
  • The bottom right vertex is at (15, 7)

To calculate the base lengths:

  1. The length of the top base can be calculated as: \( \text{Top base} = \text{Top right} - \text{Top left} = 13 - 3 = 10 \text{ feet} \)

  2. The length of the bottom base can be calculated as: \( \text{Bottom base} = \text{Bottom right} - \text{Bottom left} = 15 - 1 = 14 \text{ feet} \)

Since the designer wants to find the area by composing a rectangular shape, we focus on the bottom base.

Thus, the length of the base of the newly composed rectangle is: 14 feet.