Mathematics Questions and Answers – Mensuration – Area of General Quadrilaterals

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Mensuration – Area of General Quadrilaterals”.

1. Find the area of the given quadrilateral.

a) 26cm2
b) 27cm2
c) 29cm2
d) 25cm2
View Answer

Answer: b
Explanation: Area of general quadrilateral = \(\frac{1}{2}\) × (h1 + h2) × d  [d – diagonal of quadrilateral]
= \(\frac{1}{2}\) × (4 + 2) × 9
= 27cm2.
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2. Find the height of the quadrilateral if the area is 144cm2.

a) 24 cm
b) 12 cm
c) 22 cm
d) 11 cm
View Answer

Answer: a
Explanation: Area of general quadrilateral = \(\frac{1}{2}\) × (h1 + h2) × d  (d – diagonal of quadrilateral)
⇒ 144 = \(\frac{1}{2}\) × (8 + 4) × d
⇒ d = 24 cm.

3. The area of quadrilateral PQRS is 228cm2. Find length of QA.

a) 16 cm
b) 9 cm
c) 8 cm
d) 18 cm
View Answer

Answer: d
Explanation: Area of general quadrilateral = \(\frac{1}{2}\) × (h1 + h2) × d  (d – diagonal of quadrilateral)
⇒ 228 = \(\frac{1}{2}\) × (h1 + 20) × 12
⇒ l(QA) = 18 cm.
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4. Find the area of the shaded region. The length of the diagonal DB is 8 cm. The perpendicular distances from the vertices to the diagonal DB are 4 cm and 3 cm. The length of segment BC is 6 cm. (π = 3.14)

a) 21.87cm2
b) 9.87cm2
c) 13.87cm2
d) 17.87cm2
View Answer

Answer: c
Explanation: Area of shaded region = Area of general quadrilateral – Area of semicircle
= \(\frac{1}{2}\) × (h1 + h2) × d – \(\frac{\pi}{2}\) × (r)2 = \(\frac{1}{2}\) × (4 + 3) × 8 – \(\frac{\pi}{2}\) × (3)2 = 13.87cm2.

5. Find the area of pentagon PQRSA. The perpendicular distances from the vertices to the diagonal PR are 5 cm and 2 cm.
Given: l(PR) = 10 cm, l(PA) = 8 cm, l(SA) = 7cm.

a) 7cm2
b) 6cm2
c) 8cm2
d) 5cm2
View Answer

Answer: a
Explanation: Area of pentagon PQRSA = Area of Quadrilateral PQRS – Area of Triangle PAS
= \(\frac{1}{2}\) × (h1 + h2) × d – \(\frac{1}{2}\) × b × h = \(\frac{1}{2}\) × (5 + 2) × 10 – \(\frac{1}{2}\) × 8 × 7 = 7cm2.
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Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter