Question

The shape of the top surface of a table is a trapezium. Find its area
if its parallel sides are 1 m and 1.2 m and perpendicular distance
between them is 0.8 m.​
plz ans. me fast exam is going on

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { {Given:}} }} }$

• Parallel sides of the top surface = 1 m and 1.2 m

• Distance between its parallel sides = 0.8 m

$\underline{ \underline{ \Large \pmb{\sf { {To \: calculate:}} }} }$

• Area of the top surface.

$\underline{ \underline{ \Large \pmb{\sf { {Calculation:}} }} }$

✰ Here, we are given that the shape of the top surface of a table is a trapezium. And, the parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m. We have to find the are of the top surface. Basically, here we have to apply the area of the trapezium as the shape of the top surface of a table is a trapezium. By using the formula, we'll get the area of its top surface.

⠀⠀⠀⠀⠀_____________

As we know that,

${\underline {\boxed {\bf { Area_{(Trapezium)} = \dfrac{1}{2} \times (a+b) \times altitude } }}}$

Where,

• (a+b) = Sum of parallel sides

• Altitude = Distance between the parallel sides.

Inserting the values,

$\longrightarrow \sf { Area_{(Top \: Surface)} = \dfrac{1}{2} \times (1+1.2) \times 0.8 \: {m}^{2} }$

$\longrightarrow \sf { Area_{(Top \: Surface)} = \dfrac{1}{2} \times 2.2 \times 0.8 \: {m}^{2} }$

$\longrightarrow \sf { Area_{(Top \: Surface)} = \dfrac{1}{\cancel{2}} \times \dfrac{22}{10} \times \dfrac{\cancel{8}}{10} \: {m}^{2} }$

$\longrightarrow \sf { Area_{(Top \: Surface)} = \dfrac{22}{10} \times \dfrac{4}{10} \: {m}^{2}}$

$\longrightarrow \sf { Area_{(Top \: Surface)} = \dfrac{22 \times 4}{10 \times 10} \: {m}^{2}}$

$\longrightarrow \sf { Area_{(Top \: Surface)} = \dfrac{88}{100} \: {m}^{2}}$

$\longrightarrow \boxed{ \pmb{ \rm \red{ Area_{(Top \: Surface)} = 0.88 \: {m}^{2}}} }$

Therefore, area of the top surface of the table is 0.88 m².

Answer 2

$\frak{Given}\begin{cases} \sf{The \:Distance \:between \:\parallel \:or\:Height \:is\:0.8m\:}\\\sf{Two\:Parallel \:Sides\:of\:Trapezium \:are\:1m\:\&\:1.2m}\end{cases}$

Need to find: The Area of Trapezium.

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❍ Formula for Area of Trapezium is given by :

$\underline{\frak{Diagram:}}$

$\setlength{\unitlength}{1.1cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){ \bf A }\put(3,2.4){ \bf B }\put(-0.3,-0.3){ \bf D }\put(4,-0.3){ \bf C }\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){ \bf 0.8\ m }\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){ \bf 1.2\ m }\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){ \bf 1\ m }\end{picture}$ ⠀⠀

⠀⠀⠀$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \bigg( \dfrac{1}{2} \times (a + b) \times h\bigg)}}}}$

Where,

• a and b are the two parallel sides and h is distance between two parallel sides or height of trapezium.⠀⠀⠀⠀

$\dag\;{\underline{\frak{Now,\: Substituting\:values\:in\;formula,}}}$

$:\implies\sf Area = \dfrac{1}{2}(1 + 1.2) \times 0.8 \\\\\\:\implies\sf Area = \dfrac{1}{\cancel {2}} \times (1 + 1.2) \times \cancel {0.8} \\\\\\:\implies\sf Area = (1 + 1.2) \times 0.4\\\\\\:\implies\sf Area = 2.2 \times 0.4 \\\\\\:\implies{\underline{\boxed{\frak{\pink{Area = 0.88\;m^2}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \;the\;Area\; of\;Trapezium \;is\;\bf{ 0.88\;m^2}.}}}.$

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