Question

b) If the area of a trapezium is 98 cm and parallel sides are 6 cm and 8 cm, respectively, then the height of the trapezium is​

Answer 1

Answer:

Let the parallel sides of trapezium be 'a' and 'b' and the distance between them i.e. the height of trapezium be 'h'.

Therefore area of trapezium is given by

=1/2 *(sum of parallel side)*(distance between parallel side i.e. height of trapezium) ……(1)

Now take 'a'=12 & 'b'=8 …. (Sides are given)

Therefore,

Sum of parallel sides=a+b=12+8…. (2)

Sum of parallel side=20cm

Area=60 cm^2 …..(given) …..(3)

Putting (2) & (3) in (1) we get,

60=1/2 * 20*h

h=60/10

h=6cm

Therefore height of trapezium is 6cm.

Step-by-step explanation:

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Answer 2

$\underline{\underline{\textsf{\maltese\:\: {\orange{Given :}}}}}$

☘️ Area of trapezium = 98cm²

☘️ Length of 1st parallel side (a) = 6cm

☘️ Length of 2st parallel side (b) = 8cm

$\underline{\underline{\textsf{\maltese\:\: {\orange{To Find :}}}}}$

☘️ Height of trapezium (h) = ?

$\underline{\underline{\textsf{\maltese\:\: {\orange{Concept Implemented :}}}}}$

☘️ $\star \; \underline{\textbf{Area of trapezium = \dfrac{1}{2} (Sum of parallel sides) Height}} \; \star$

$\underline{\underline{\textsf{\maltese\:\: {\orange{Solution :}}}}}$

$\underline{\textbf{Area of trapezium = \dfrac{1}{2} (Sum of parallel sides) Height}}$

${\textbf{Area of trapezium = \dfrac{1}{2} (a + b) h} }$

⇒ 98cm² = $\dfrac{1}{2}$ (6cm + 8cm) h

⇒ 98cm² = $\dfrac{1}{2}$ (14cm) h

⇒ 98cm² = 7cm × h

⇒ $\sf\dfrac{98 \; cm^2}{7\;cm}$ = h

⇒ 14cm = h

∴ h = 14cm

$\underline{\underline{\textbf{ \therefore Height of trapezium (h) is 14cm. }}}$