Question

give me answer of this question

Answer 1

Answer:

196 cm²

Step-by-step explanation:

Here in the figure, you can see that

Area of Shaded Region = Area of Trapezium - (Area of Four Sectors)

Lets find the area of four sectors first

Radii of each sector is given 7 cm

We know that area of sector

$=\frac{\theta}{360^o}\pi (radius)^2$

Therefore Area of Four sectors with

Radius = 7 cm and Ф = ∠A, ∠B, ∠C and ∠D

$=\frac{\angle A}{360^o}\pi (7)^2+\frac{\angle B}{360^o}\pi (7)^2+\frac{\angle C}{360^o}\pi (7)^2+\frac{\angle D}{360^o}\pi (7)^2$

$=\frac{1}{360^o}\pi (7)^2 (\angle A + \angle B + \angle C + \angle D)$

We know that Sum of all interior angles in a quadrilateral is 360°

∴ Putting ∠A + ∠B + ∠C + ∠D = 360°

$\frac{1}{360^o}\pi (7)^2 \times 360^o$

$=\pi (7)^2$

$\frac{22}{7}\times 7\times 7$

= 154 cm²

∴ Area of four sectors = 154 cm² -------- ( i )

Now Area of Trapezium

= 1/2 × sum of parallel sides × distance between them

= 1/2 × (18 + 32) × 14

= 1/2 × 50 × 14

= 50 × 7

Area of Trapezium = 350 cm² ------- ( ii )

Area of Shaded Region = Area of Trapezium - (Area of Four Sectors)

                                       = 350 cm² - 154 cm²     [From ( i ) and ( ii )]

                                       = 196 cm²

Hence, Area of shaded region is 196 cm²