Convex Quadrilateral ABCD has AB = 3, BC = 4, CD = 13, AD = 12 GMAT Problem Solving

Question: Convex quadrilateral ABCD has AB = 3, BC = 4, CD = 13, AD = 12, and angle ABC=90°, as shown. What is the area of the quadrilateral?

(A) 30
(B) 36
(C) 40
(D) 48
(E) 58.5

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

AC = 5,
Triangle ACD forms another right angle triangle. Standard 5,12,13 triangle.
Area of ABC = 1/2 * Base * Height = 1/2 * 4 * 3 = 6
Area of ACD = 1/2 * 12 * 5 = 30
Total area = 6+30 = 36

Approach Solution 2:

Note that by the pythagorean theorem, . Also note that is a right angle because is a right triangle. The area of the quadrilateral is the sum of the areas of and which is equal to
3*4/2+5*12/2= 6+30= 36

“Convex quadrilateral ABCD has AB = 3, BC = 4, CD = 13, AD = 12, and”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018 Quantitative Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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