Question

Find the area of the shaded region. Here ABC is a right-angled triangle where AB = 8 cm,
BC = 6 cm and ADC, BEC and AFB are semicircles.​

Answer 1

Answer:

which is shaded here say

Answer 2

Given:

ABC is a right-angled triangle where AB = 8 cm,  BC = 6 cm and ADC, BEC and AFB are semicircles.​

To find:

The area of the shaded region

Solution:

Finding the area of the ΔABC:

We know,

• Area of a triangle = ½ × base × height

∴ Area of triangle ABC is,

= ½ × AB × BC

substituting the given values of AB & BC

= ½ × 8 × 6

= 4 × 6

= 24 cm²

Finding the area of semi-circle AFB:

We know,

• Area of a semi-circle = ½ × $\pi r^2$

∴ Area of semi-circle AFB is,

= ½ × $\pi r^2$

substituting the value of r = $\frac{diameter}{2} = \frac{AB}{2} = \frac{8}{2} = 4$

= ½ × $\frac{22}{7}$ × 4²

= $\frac{22\times 16}{14}$

= 25.14 cm²

Finding the area of semi-circle BEC:

∴ Area of semi-circle BEC is,

= ½ × $\pi r^2$

substituting the value of r = $\frac{diameter}{2} = \frac{BC}{2} = \frac{6}{2} = 3$

= ½ × $\frac{22}{7}$ × 3²

= $\frac{22\times 9}{14}$

= 14.14 cm²

Finding the area of semi-circle ADC:

Using the Pythagoras theorem in Δ ABC, we get

AB² + BC² = AC²

⇒ 8² + 6² = AC²

⇒ 64 + 36 = AC²

⇒ 100 = AC²

⇒  AC = √100

⇒ AC = 10 cm

∴ Area of semi-circle ADC is,

= ½ × $\pi r^2$

substituting the value of r = $\frac{diameter}{2} = \frac{AC}{2} = \frac{10}{2} = 5$

= ½ × $\frac{22}{7}$ × 5²

= $\frac{22\times 25}{14}$

= 39.28 cm²

Finding the area of the shaded region:

∴ The area of the shaded region is,

= [Area of triangle ABC] + [Area of semi-circle AFB] + [Area of semi-circle BEC] + [Area of semi-circle ADC]

= [24 cm²] + [25.14 cm²] + [14.14 cm²] + [39.28 cm²]

= 102.56 cm²

Thus, $\boxed{\boxed{\bold{Area\:of\:shaded\:region\:is\:\underline{102.56\:cm^2}}}}.$

------------------------------------------------------------------------------------

Also View:

Find the area of the shaded region in the given figure

https://brainly.in/question/24123771

Calculate the area of the shaded region

https://brainly.in/question/5373342

Find the areas of the shaded regions ​

https://brainly.in/question/14574343

Find the area of the shaded region .​

https://brainly.in/question/20312768