Question

In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is ​

Answer 1

Answer:

your ans is given in attached pic....

Answer 2

Given :- ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively.

To Find :- The area of shaded region .

Construction :- Join mid point H and F .

So,

→ Shaded area = Semi circle area inside rectangle ABFH + (Rectangle HFCD - 2 quadrant area)

since,

→ HF = AB = 14 cm .

So,

→ Diameter of semi - circle = 14 cm

then,

→ Radius of semi - circle = diameter / 2 = 14/2 = 7 cm

and,

→ DG = GC { G is mid point of CD }

→ DG = GC = 7 cm

So,

→ Radius of quadrant = 7 cm .

We know that,

• Area of rectangle = Length * Breadth
• Area of semi - circle = (1/2)πr²
• Area of quadrant = (1/4)πr² .

then,

→ Shaded area = Semi circle area inside rectangle ABFH + (Rectangle HFCD - 2 quadrant area)

putting all values now we get,

→ Shaded area = (1/2)π(7)² + [14 × 7 - 2 × (1/4) × π × (7)²]

→ Shaded area = (1/2)*(22/7)*49 + [98 - (1/2)*(22/7)*49]

→ Shaded area = 98 + (1/2)*(22/7)*49 - (1/2)*(22/7)*49 { Both will be cancel .}

→ Shaded area = 98 cm² (Ans.)

Therefore, The area of the shaded portion is equal to 98 cm² .

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