Question
1.
2.
3.
4.
Answer (Detailed Solution Below)
Option 3 : $204$ cm²
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Detailed Solution
सही उत्तर $204$ cm² है।
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prepsnap.in • Part -AQuestion:
A trapezium has parallel sides of $24$ cm and $10$ cm, and its non-parallel sides are $15$ cm and $13$ cm. What is its area? / एक समलंब चतुर्भुज की समांतर भुजाएँ $24$ सेमी और $10$ सेमी हैं तथा असमांतर भुजाएँ $15$ सेमी और $13$ सेमी हैं। इसका क्षेत्रफल क्या है?
1.
$196$ cm²
2.
$216$ cm²
3.
$204$ cm²
4.
$228$ cm²
Correct Answer: $204$ cm²
The difference of the parallel sides is $14$. Dropping perpendiculars, the projection of the $15$ cm side is $x$ with $x^{2}+h^{2} = 225$ and $(14-x)^{2}+h^{2} = 169$; subtracting gives $196-28x = -56 \Rightarrow x = 9$, $h = 12$. Area $= \frac{24+10}{2}\times12 = 204$ cm². / ऊँचाई $12$ सेमी; क्षेत्रफल $= 17\times12 = 204$ सेमी²। Option (a) is the trap of taking the height as $11$ cm from a wrong projection.
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