Question

find the Area of polygons ​

Answer 1

||GIVEN||

• ABCD is a Trapezium.
• AB = 15cm, CD = 25cm & AD = 16cm
• In Trapezium, Rectangle EFGH is inscribed EF = 3cm & FG = 10cm.
• Along with a circle of Diameter 7cm.

||TO FIND||

• Area of the Polygon.
• Area of Shaded Region.
• Area Remaining [Unshaded Region].

||SOLUTION||

Area of Trapezium ABCD,

$\frac{(15 + 25)}{2} \times 16 \\ 40 \times 8 \\ 320$

• Area of Trapezium ☞ 320cm²

Area of Rectangle EFGH

$3 \times 10 \\ 30$

• Area of Rectangle ☞ 30cm²

In the given Circle

Diameter = 7cm

Radius = diameter/2

R = 7/2

$\pi { (\frac{7}{2}) }^{2} \\ \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \\ 11 \times \frac{1}{2} \times \frac{7}{2} \\ \frac{77}{2} \\ 38.5$

• Area of Circle ☞ 38.5cm²

Area of Unshaded Region = Area of Rectangle+Area of Circle

$30 + 38.5 \\ 68.5$

• Area of Unshaded Region = 68.5cm²

Area of Shaded Region = Area of Polygon-Area of Unshaded Region

$320 - 68.5 \\ 281.5$

• Area of Shaded Region ☞ 281.5cm²

$\boxed{\sf{Area\;of\; Trapezium = \frac{(a+b)}{2}h}}$

$\boxed{\sf{Area\;of\; Rectangle = Length×Breadth}}$

$\boxed{\sf{Area\;of\; Circle = \pi{r}^{2}}}$

$\tt{@MrMonarque}$

Hope It Helps You ✌️