Question in attachment
Answers
Answer:
1. AEFD = 196 cm²
2. ABC = 49 cm²
3. semicircle = 77 cm²
4. shaded region = 70 cm²
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Given :
BC = 14cm
AB = ½ BC
AB = ½ x 14 = 7cm
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To Find :
(i) Area of Quad AEFD
(ii)Area of ΔABC
(iii)Area of Semicircle
*Need to find the area if Shaded region as well*
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Solution :
(i) In Quad AEFD ,
AE ⊥ EF
DF ⊥ AD
AD ⊥ AE
All the Angles in the quadrilateral are 90°
Therefore the quadrilateral so formed is Square
⇒AEFD is a square of Side , 7 +7 = 14cm
Area of AEFD = (Side)²
= (14)²cm²
= 196cm²
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(ii) In ΔABC,
Height = AB = 7cm
Base = BC = 14cm
Area of ΔABC = ½ x Base x Height
= ½ x 7 x 14
= 49cm²
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(iii) Area of Semicircle
r = 7cm
Area of semicircle = ½ x πr²
= ½ x 22/7 x 7 x 7
= 77cm²
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(iv) In Rectangle BEFC
BE = CF = Breadth of the rectangle
BC = EF = Length of the rectangle
We can clearly notice that semicircle is inscribed in the rectangle
Therefore area of shaded region in BEFC
= Area of Rectangle - Area of semicircle
= (14 x 7 - 77)cm²
= (98 - 77)cm²
= 21cm² ----(1)
In Rectangle ABCD
Area of shaded region
= Area if Rectangle - Area of ΔABC
= (14 x 7 - 49)cm²
=(98 - 49)cm²
=49cm² ----(2)
To get the total area of shaded region we add (1) and (2)
(49 + 21)cm²
=70cm²
Hence the area of shaded region = 70cm²
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