Question

Find the area of yellow shaded region in which AC = 33 cm, BC = 24 cm, AD =

12 cm and BD = 5 cm and ADB = 90

0 ∠ .(Take √35 = 5.91)
See I have post the pic.
Now please answer this question​

Answer 1

I have attached the given diagram.

We are given the following sides of the triangle,

• AC = 33 cm
• BC = 24 cm
• AD = 12 cm
• BD = 5 cm
• ∠ADB = 90°

Also, we have to take √35 = 5.91

Now, We have to find the area of the yellow coloured shape. Clearly it can be found by subtracting the area of ∆ADB from the area of ∆ABC.

But we need the third side of ∆ABC, i.e., AB which can be found using the Pythagoras theorem in ∆ADB,

In ∆ADB,

using Pythagoras theorem,

⇒ Hypotenuse² = Base² + Perpendicular²

⇒ AB² = BD² + AD²

⇒ AB² = 5² + 12²

⇒ AB² = 25 + 144

⇒ AB² = 169

⇒ AB = 13

Now, In ∆ABC using heron's formula, we have

• a = AB = 13 cm
• b = BC = 24 cm
• c = AC = 33 cm

Also,

• Semi-perimeter, s = (a + b + c)/2 = 35 cm

Now,

⇒ ar(∆ABC) = √{ s(s - a)(s - b)(s - c) }

⇒ ar(∆ABC) = √{ 35(35 - 13)(35 - 24)(35 - 33) }

⇒ ar(∆ABC) = √( 35 × 22 × 11 × 2 )

⇒ ar(∆ABC) = 22√35

⇒ ar(∆ABC) = 130.02 cm²

Similarly, In ∆ADB, Since it is a right angled triangle , so

⇒ ar(∆ADB) = 1/2 × base × height

⇒ ar(∆ADB) = 1/2 × BD × AD

⇒ ar(∆ADB) = 1/2 × 5 × 12

⇒ ar(∆ADB) = 5 × 6

⇒ ar(∆ADB) = 30 cm²

So, Area of shaded region (yellow coloured region)

⇒ ar(∆ABC) - ar(∆ADB)

⇒ 130.02 - 30

⇒ 100.02 cm²

Hence,

Area of yellow shaded region is 100.02 cm²

Answer 2

Two semicircles are drawn with AB and BC as their diameters respectively. Find the shaded area. ... Get Instant Solutions, 24x7. No