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:

14 cm.

Step-by-step explanation:

Given:

• Area of trapezium = 98 cm²
• Parellel sides = 6 cm and 8 cm

To find:

• Height of trapezium (h) = ?

Solution:

We remember that area of trapezium = ½ × (sum of parallel sides) × height.

$\Longrightarrow\:\sf{98\:=\:\dfrac{1}{2}\:\times\:(8\:+\:6)\:\times\:h}$

$\:$

$\Longrightarrow$ 98 × 2 = 14 × h

$\:$

$\Longrightarrow\:\sf{\dfrac{98\:\times\:\cancel{2}}{\cancel{14}}\:=\:h}$

$\:$

$\Longrightarrow\sf{\underline{\underline{\therefore\:Height\:=\:14\:cm.}}}$

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

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