Question:

What is the area of quadrilateral ABCD shown?

1. 480
2. 525
3. 550
4. 576
5. 1152

“What is the area of quadrilateral ABCD shown?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review 2022". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
Area of quadrilateral ABCD = Area of Triangle ADC + Area of Triangle ABC

We need to find the hypotenuse of the triangle ADC.

AC^2 = 16^2+12^2
= 256 + 144
= 400
AC = 20

Area of triangle ADC = 1/2* 16 * 12
Area of triangle ADC = 96

Area of triangle ABC. Here, we have to find the base length, BC.
We already know AC = 20

52^2= 20^2+BC^2
BC^2= 52^2-2^2
BC = 48

Area of triangle ABC = 1/2* 48 * 20
Area of triangle ABC = 480

Therefore, total area = 480 + 96
total area = 576

Correct Answer: D

Approach Solution 2:
Both △ADC and △ACB are right angled triangle...

△ADC is a expanded form of 3−4−5 triangle , So, AC=20

So, BC= root 52^2−20^2= 48

Thus, Area of the figure is
1/2∗12∗16+1/2∗20∗48= 96+480= 576

Correct Answer: D

Approach Solution 3:
Triangle ADC is a right angled triangle which is right angled at B
The sides of the triangle form pythagorean triplets.

AD = 12, DC = 16, therefore AC = 20

Triangle ABC is a right angled triangle which is right angled at C
The sides of the triangle form pythagorean triplets.

AC = 20, AB = 52, therefore BC = 48

Area ABCD = Area ABC + Area ADC

= (1/2)*20*48 + (1/2)*12*16
= 480 + 96
= 576

Correct Answer: D

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