In the given figure- ABCD is a trapezium of area 24-5 cm2- If AD - BC- - DAB-90-AD-10 cm-BC-4 cm and ABE is quadrant of a circle- then find the area of the shaded region-

Area of Trapezium ABCD = AB2( AD + BC) [ 24.5= AB 2 ( 10+4 ) ...

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Byju's Answer

Standard X

Mathematics

Areas of Combination of Plane Figures

In the given ...

Question

In the given figure, $A B C D$ is a trapezium of area $24.5 c m^{2}$ . If $A D ∥ B C, ∠ D A B = 90^{\circ}, A D = 10 c m, B C = 4 c m$ and $A B E$ is quadrant of a circle. then find the area of the shaded region.

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Solution

Area of Trapezium $A B C D = \frac{A B}{2} (A D + B C)$
$\begin{matrix} 24.5 = \frac{A B}{2} (10 + 4) & [\begin{matrix} ∵ A r e a o f T r a p e z i u m A B C D = 24.5 A D = 10, B C = 4 \end{matrix}] 49 = A B (14) A B = 3.5 c m \end{matrix}$
Radius of Quadrant of circle AB = 3.5 cm
Area of Quadrant of circle $= \frac{π r^{2}}{4}$
$= \frac{1}{4} \times \frac{22}{7} \times 3.5 \times 3.5 \Rightarrow 9.625 c m^{2}$
Area of shaded Region = Area of Trapezium - Area of Quadrant of circle
$\begin{matrix} = 24.5 - 9.625 = 14.875 c m^{2} \end{matrix}$

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Similar questions

Q. In the given figure, ABCD is a trapezium of area 24.5 cm² , If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle, then find the area of the shaded region. [CBSE 2014]

In Fig. ABCD is a trapezium of area $24.5 c m^{2}$ . In it, $A D ∥ B C$ , $∠ D A B = 90^{\circ}$ , AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region. (Take $π = \frac{22}{7}$ )

A B C D

is a trapezium of area

24.5

sq. cm. In it,

A D ∥ B C, ∠ D A B = 90^{\circ}, A D = 10 c m

and

B C = 4 c m

. If

A B E

is a quadrant of a circle, find the area of the shaded region.

[Take π = \frac{22}{7}]

Q. ABCD is a trapezium of area 24.5 cm. In it

A D ∥ B C

D A B = 90^{\circ}

, AD = 10 cm and BC = 4 cm, If ABE is a quadrant of circle, find shaded region.

Q. In fig. is a trapezium of area

24.5 {c m}^{2}

,In it , AD||BC,

∠ D A B = 90^{0}

, AC=10 cm and BC=4 cm.If ABE is a quadrant of a circle, the area of the shaded region.

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In the given figure, ABCD is a trapezium of area 24.5cm2. If AD∥BC,∠DAB=90∘,AD=10cm,BC=4cm and ABE is quadrant of a circle. then find the area of the shaded region.

Area of Trapezium ABCD=AB2(AD+BC)24.5=AB2(10+4)[∵AreaofTrapeziumABCD=24.5AD=10,BC=4]49=AB(14)AB=3.5cmRadius of Quadrant of circle AB = 3.5 cmArea of Quadrant of circle =πr24=14×227×3.5×3.5⇒9.625cm2Area of shaded Region = Area of Trapezium - Area of Quadrant of circle=24.5−9.625=14.875cm2

In the given figure, $A B C D$ is a trapezium of area $24.5 c m^{2}$ . If $A D ∥ B C, ∠ D A B = 90^{\circ}, A D = 10 c m, B C = 4 c m$ and $A B E$ is quadrant of a circle. then find the area of the shaded region.