Question

find the area of the shaded region in each of the following figures in which the dimensions are given in centimetres​

Answer 1

Answer:

ii) 217.70 cm²

iii) 72 cm²

Step-by-step explanation:

ii) We need to get the area of each of the shapes in the figure.

• we need to get the height using Pythagorean theorem.

       h = √(10² - 8²) = 6

       Area = 1/2 × 6 × 8 = 24 cm²

• A = √s(s - a)(s - b)(s - c)

       s = (10 + 10 + 10)/2 = 15 cm

       A = √15(15 - 10)(15 - 10)(15 - 10)

       A = √1875 = 43.30 cm²

• A = Side²

     A = 3² = 9 cm²

• h = √(5² - 4²) = 3 cm

       A = 1/2 × 3 × 4 = 6 cm²

• Area of the rectangle = 25 × 12 = 300 cm²

Area of the figure = 300 - (24 + 43.30 + 9 + 6) = 217.70 cm²

iii) Area of the rectangle = 8 × 12 = 96 cm²

Area of the two right angled triangles = 2 (1/2 × 6 × 4) = 24 cm²

Area of the figure = 96 - 24 = 72 cm²