Question

ABC is a diameter of a circle and ab parallel to dc if ab is 50 cm and DC 40 cm find the distance between a b and c d also calculate the area of ABCD​

Answer 1

Step-by-step explanation:

Given-

ABCD is a trapezium. AB∥DC  and AB=18 cm, DC=32 cm. 

There are 4 arcs centring the vertices A,B,C,D with radius r=7 cm.

To find out - area of shaded region

Solution-

Area of trapezium =21× sum of the parallel sides × distance between the parallel sides.=21×(AB+CD)×14=21×(18+32)×14cm2=350 cm2.

Let us take the angles of the trapezium as a at A,b at B,c  at C and d at D.

Now the given arcs form 4 sectors. 

Together they form a circle of radius r=7 cm as a+b+c+d=360o.

∴  The area of the sectors=area of circle with radius (r=7cm) =π×r2=722×72=154 cm2.

∴  Area of shaded region = area of trapezium − area of circle

=(350−154)=196 cm2.

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