In a trapezium ABCD Show fig. 15.10, angle d=90, B
Answers
Answer:
Given the dimension of a trapezium except the height✓
Firstly we need to. calculate out the height of the trapezium so as to find the area of the trapezium ✓
From the above information we find that ADC forms a right angle triangle and Right angled at D
\bold{so \: by \: applying \: pythagoras \: theorem \: we \: can\: find \: the \: height\: f \: the \: triangle \: }sobyapplyingpythagorastheoremwecanfindtheheightfthetriangle
\begin{gathered}= > ac ^{2} \: = ad^{2} + dc^{2} \\ \\ = > 26 ^{2} = 24^{2} + ad ^{2} \\ \\ = > ad = \sqrt{26 ^{2} - 24 ^{2} } \\ \\ = > ad = \sqrt{676 - 576} \\ \\ = > ad = \sqrt{100} = 10 \: cm\end{gathered}
=>ac
2
=ad
2
+dc
2
=>26
2
=24
2
+ad
2
=>ad=
26
2
−24
2
=>ad=
676−576
=>ad=
100
=10cm
So from the above calculation we find the height of the triangle is 10 cm And it's clear that the height of the triangle is equal to the height of the trapezium
So the area if the trapezium is as follows
\begin{gathered}\bold{\red{\: area = \frac{1}{2} \times (ab \: + dc) \times ad }}\\ \\ = >area = \frac{(18 + 24) \times 10}{2} \\ \\ = > area = \frac{420}{2} \\ \\ = > \bold{\boxed{\red{\boxed{area \: = 210cm ^{2} }}}}\end{gathered}
area=
2
1
×(ab+dc)×ad
=>area=
2
(18+24)×10
=>area=
2
420
=>
area=210cm
2
So the area if the trapezium is 210 cm²
Explanation:
hope it will help you