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NTPC Graduate Tier 1 2025 Shift-1 📅 06 May, 2025

In quadrilateral ABCD, AB = 17 cm, BC = 8 cm, CD = 9 cm, AD = 12 cm, and AC = 15 cm. What is the area (in cm²) of the quadrilateral?

A
105
B
114
C
118
D
121
Result Summary
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NTPC Graduate Tier 1
2025 • 06 May, 2025 • Shift-1
In quadrilateral ABCD, AB = 17 cm, BC = 8 cm, CD = 9 cm, AD = 12 cm, and AC = 15 cm. What is the area (in cm²) of the quadrilateral?
Correct Answer
114
Triangle Partitioning: The diagonal AC completely splits the complex quadrilateral into two distinct triangles: Triangle ABC and Triangle ADC.Area of First Tria......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Mensuration
Pg. No -
💡 Analysis & Explanation
Triangle Partitioning ▼
The diagonal AC completely splits the complex quadrilateral into two distinct triangles: Triangle ABC and Triangle ADC.
Area of First Triangle ▼
Triangle ABC possesses sides measuring 8, 15, and 17. This represents a classic Pythagorean triple, making it a right-angled triangle. Its area is calculated as (1/2) * Base * Height = (1/2) * 8 * 15 = 60 sq cm.
Area of Second Triangle ▼
Similarly, Triangle ADC features sides of 9, 12, and 15, which is also a Pythagorean triple (a multiple of 3-4-5). Its area is (1/2) * 9 * 12 = 54 sq cm.
Total Area Calculation ▼
Summing the separate areas of the two component triangles gives 60 + 54 = 114.
Conclusion ▼
The total geometric area of the entire quadrilateral is 114 cm².
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