Question

Two parallel sides of a trapezium are 12 cm and 8cm and the distance between the parallel sides is 5 cm.The area of the trapezium is ​

Answer 1

$\setlength{\unitlength}{1.5cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf D }\put(-0.3,-0.3){ \bf B }\put(4,-0.3){ \bf C }\put(4.2,0){\vector(0,0){2.2}}\put( 4.2, 0){\vector(0, - 1){0.1}}\put(4.4,1){ \bf 5 cm }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.5, - 0.9){ \bf 12 cm }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 8 cm }\end{picture}$

• Parallel sides of trapezium = 12 cm and 8 cm.

• Distance between two parallel sides (height), h = 5 cm

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\star\;{\boxed{\sf{\purple{Area_{\;(trapezium)} = \dfrac{1}{2} \times (sum\:of\: parallel\;sides) \times height}}}}$

Putting values,

$:\implies\sf \dfrac{1}{2} \times (12 + 8) \times 5$

$:\implies\sf \dfrac{1}{ \cancel{2}} \times \cancel{20} \times 5$

$:\implies\sf 10 \times 5$

$:\implies{\boxed{\frak{\pink{50\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Area\;of\; trapezium\;is\; \bf{50\;cm^2}.}}}$

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

A trapezium is a quadrilateral having four sides and one set of parallel sides.

• Sum of all the four angles of the trapezium is equal to 360°.

• A trapezium has two parallel sides and two non-parallel sides.

• The diagonals of regular trapezium bisect each other.

Answer 2

Given ,

The two parallel sides of a trapezium are 12 cm and 8 cm

The distance between the parallel sides is 5 cm

We know that , the area of trapezium is given by

$\boxed{ \tt{Area = \frac{1}{2} \times (sum \: of \: parallel \: sides} \times height}$

Thus ,

Area = 1/2 × (12 + 8) × 5

Area = 1/2 × 20 × 5

Area = 10 × 5

Area = 50 cm²

Therefore , the area of trapezium is 50 cm²

______________ Keep Smiling ☺