Question

Find the area of a trapezium-shaped window if the lengths of the parallel sides are 47 cm and 69 cm and the perpendicular distance between them is 23cm​

Answer 1

Answer ::

The area of trapezium is 1334m².

Step-by-step explanation ::

To Find :-

• The area of trapezium

Solution :-

Given that,

• The top of a table is in the shape of a trapezium.
• The lengths of the parallel sides are 47cm and 69cm
• The perpendicular distance between them is 23cm

As we know that,

Area of trapezium = 1/2 × ( sum of parallel sides ) × distance between them,

⟾ Area = 1/2 × ( 47 + 69 ) × 23

⟾ Area = 1/2 × 116 × 23 . . . dividing 116 and 2 with 2

⟾ Area = 1 × 58 × 23

⟾ 1334 ★

The area of trapezium is 1334².

More Information

Some more important formulas & properties related to trapezium :-

Formulas :-

• Perimeter of trapezium = Sum of all sides of trapezium.
• Area of trapezium = 1/2 × ( sum of all parallel sides ) × distance between them.

Properties of an irregular trapezium :-

• One pair of opposite sides is parallel.
• two pairs of adjacent angles ( which form a pair of consecutive interior angles ) are supplementary [ 180° ]

Answer 2

$\mathfrak{ \pink{ \underline{ \blue{ \large{Correct \: Question: }}}}}$

Find the area of a trapezium-shaped window if the lengths of the parallel sides are 47 cm and 69 cm and the perpendicular distance between them is 23cm

$\mathfrak{ \pink{ \underline{ \blue{ \large{ Given:}}}}}$

• Parallel sides of trapezium = 47 cm and 69 cm
• Height of trapezium = 23 cm

$\mathfrak{ \pink{ \underline{ \blue{ \large{To \: Find: }}}}}$

• Area of trapezium

$\mathfrak{ \pink{ \underline{ \blue{ \large{ Solution: }}}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\ \mathfrak{ \underline{ \green{Formula \: to \: calculate \: the \: area \: of \: trapezium \: }}}$

$\boxed{ \boxed{ \star \: \: \: \: \: \:{ \large { \red{ \mathfrak{area = \frac{sum \: of \: parallel \: sides}{2} \times height}}}}}}$

According to question,

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \:\: \: {area = \frac{47+69}{2} \times 23}}$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \:\: \:area = \frac{116}{2} \times 23}$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \:\: \:area = 58 \times 23}$

$\large{ \sf \longmapsto \: \: \: \: \: \: \: \:\: \: \boxed{ \boxed{ \purple{ \mathfrak{area = 1334\: {cm}^{2} }}}}}$

$\mathfrak{ \pink{ \underline{ \blue{ \large{ Hence:}}}}}$

The area of trapezium is 1334 cm²