A trapezium has height 10cm and area 180cm^2. If one parallel side is 12 cm, what is the other side?
A trapezium has height 10cm and area 180$ \text{cm}^2$. If one parallel side is 12 cm, what is the other side?
एक समलम्ब चतुर्भुज की ऊँचाई 10 सेमी और क्षेत्रफल 180 $ \text{cm}^2 $ है। यदि एक समांतर भुजा 12 सेमी है, तो दूसरी समांतर भुजा कितनी होगी?
Detailed Solution & Logic
Correct Answer:
24 cm
We are given:
-
Height of trapezium $h = 10$ cm
-
Area $A = 180 , \text{cm}^2$
-
One parallel side $a = 12$ cm
Let the other parallel side be $b$ cm.
Area of a trapezium formula:
$A = \frac{1}{2} \times (a + b) \times h$
Substitute the values:
$180 = \frac{1}{2} \times (12 + b) \times 10$
$180 = 5 \times (12 + b)$
$12 + b = \frac{180}{5} = 36$
b = 36 - 12 = 24
Other parallel side = 24 cm
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