the two parallel sides of a trapezium are 10 cm and 24 cm respectively ,if non parallel sides are each equal to 12 cm,find the area of the trapezium.
Answers
Area of the trapezium is 180 cm².
Step-by-step explanation:
The figure is drawn below,
From the figure, it is clear that the lengths CD and EF are each equal to 5 cm due to symmetry of the figure.
Consider Δ BCD which is a right angled triangle.
Using Pythagoras Theorem,
\begin{gathered}BC^2=CD^2+BD^2\\13^2=5^2+BD^2\\169=25+BD^2\\BD^2=169-25\\BD^2=144\\BD=\sqrt{144}=12\ cm\end{gathered}
BC
2
=CD
2
+BD
2
13
2
=5
2
+BD
2
169=25+BD
2
BD
2
=169−25
BD
2
=144
BD=
144
=12 cm
Now, area of trapezium ABCF is given as:
\begin{gathered}Area=\frac{1}{2}\times (\textrm{Sum of parallel sides}\times \textrm{Height}\\Area=\frac{1}{2}\times (10+20)\times 12\\Area=\frac{1}{2}\times 30\times 12=15\times 12=180\ cm^2\end{gathered}
Area=
2
1
×(Sum of parallel sides×Height
Area=
2
1
×(10+20)×12
Area=
2
1
×30×12=15×12=180 cm
2
Therefore, the area of the trapezium with parallel sides 10 cm and 20 cm is 180 cm².
