In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (15, 2), (15,-4)? A. 91 B. 95 C. 104 D. 117 E. 182
(A) First, we should make a rough sketch of the figure to determine its general shape. Its left side and right side are parallel, with the left side having a length of 8 and the right side having a length of 6. The distance between these two sides is 13.This figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Alternate Method (Breaking the figure apart): Without the formula for the area of a trapezoid, we can still solve the problem. We can draw two horizontal lines through the figure, one at y = 2 and one at y = -2 to divide the trapezoid into an upper triangle, a rectangle, and a lower triangle.
The upper triangle has an area of (1/2) × 4 × 13 = 26. The rectangle has an area of 4 × 13 = 52. The lower triangle has an area of 1/2 × 2 × 13 = 13.
Adding these areas, we get the area for the quadrilateral: 52 + 26 + 13 = 91.
Again, we see that the correct answer is choice (A). -------------
If the y coordinates are -2 and 6 then the length of the left side is 9 and the right side is 7 (you need to count the 0)! Area = 1/2 × (9+7) × 13 = 104 (and not 91)
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