Question

Calculate the area of the shaded region.​

Answer 1

Answer:

54 cm²

Step-by-step explanation:

In the given question:

Area of ΔABC= shaded area + area of a right angled triangle(ΔAOB)

Using Pythagoras theorem in ΔAOB,

    AB² = 12² + 5²     ⇒ AB = 13 cm

Semi-perimeter = (15 + 14 + 13)/2 = 21

 Using Heron's formula:  Ar. of ABC

⇒ Area = √(21)(21 - 15)(21 - 14)(21 - 13)

            = √(21)(6)(7)(8)

            = √7056

            = 84 cm²

Moreover, area of the right-angled triangle ΔAOB:

    Area = 1/2 base * height

             = 1/2 * AO * OB

             = 1/2 * 12 * 5

             = 30 cm²

Hence,

⇒ 84cm² = shaded area + 30cm²

⇒ 54 cm² = shaded area