Question

The lengths of parallel sides of a trapezium is 12 cm and 18 cm and it's area is 135 sq.cm then what is it's perpendicular height?​

Answer 1

Given:-

• The lengths of parallel sides of a trapezium is 12 cm and 18 cm and it's area is 135 cm².

To Find:-

• Perpendicular Height of Trapezium

Formula Used:-

• ${\boxed{\bf{Area\:of\:Trapezium = \dfrac{1}{2} \times [P_1+P_2] \times H}}}$

Here,

• $\bf P_1=$ First Parallel Side

• $\bf P_2=$ Second Parallel Side

• H = Perpendicular Height

Solution:-

$\bf :\implies\:Area\:= \dfrac{1}{2} \times [P_1+P_2] \times H$

Here,

• $\bf P_1=12$

• $\bf P_2=18$

• Area = 135cm²

Putting Values,

$\sf :\implies\:135= \dfrac{1}{2} \times [12+18] \times H$

$\sf :\implies\:135\times 2= 30 \times H$

$\sf :\implies\:30H=270$

$\sf :\implies\:H=\dfrac{270}{30}$

$\sf :\implies\:H=\dfrac{27}{3}$

$\bf :\implies\:H=9\:cm$

Hence The Perpendicular Height of Trapezium is 9cm.

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

This looks like a math homework question. I will solve your initial problem but using the sides 4, 8 and Area 30 instead.

Area formula for a trapezium (a.k.a trapezoid):

=1+22ℎ
A
=
b
1
+
b
2
2
h

Where
A
is the total area, 1
b
1
and 2
b
2
are the parallell sides of the trapezoid, and ℎ
h
is the height of the trapezoid. And we want to know what? Right, the height, or ℎ
h
. So, let’s rewrite the formula:

=1+22ℎ
A
=
b
1
+
b
2
2
h

2=(1+2)ℎ
2
A
=
(
b
1
+
b
2
)
h

21+2=ℎ
2
A
b
1
+
b
2
=
h

Now let us look at what is known:

=30
A
=
30

1=4
b
1
=
4

2=8
b
2
=
8

Finally, insert the numbers:

2⋅304+8=6012=5
2
⋅
30
4
+
8
=
60
12
=
5

Answer: ℎ=5
h
=
5

There you go. Everything you need to solve your particular problem. Now solve it! :)