Bunuel wrote:

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

Kudos for a correct solution.

800score Official Solution: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:

Area = 1/2 × (8 + 6) × 13 = 1/2 × 14 × 13 = 7 × 13 = 91.

The correct answer is choice (A).

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).

_________________

New to the Math Forum?

Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:

GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

Extra-hard Quant Tests with Brilliant Analytics