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)
Users browsing this forum: Majestic-12 [Bot] and 1 guest
You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.