Chapter 6 - Measuring Space: Perimeter and Area (Continued)

Math Solutions: Advanced Area & Sequences (End of Chapter) Chapter 6 - Measuring Space: Perimeter and Area (Continued) End-Of-Chapter Exercises Q. Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm. Solution: The perimeter of the triangle is 32 cm. Let the sides be a = 8 cm, b = 11 cm, and c . Third side c = 32 - (8 + 11) = 32 - 19 = 13 cm . The semi-perimeter s = 32 / 2 = 16 cm . Using Heron's formula: Area = √[s(s-a)(s-b)(s-c)] Area = √[16 × (16 - 8) × (16 - 11) × (16 - 13)] Area = √[16 × 8 × 5 × 3] Area = √1920 = 8√30 cm² The area of the triangle is 8√30 cm² . Q. The sides of a triangular plot are in the ratio 3:5:7; its perimeter is 300 m. Find its area. Solution: Let the sides of the triangle be 3x , 5x , and 7x . Perimeter = 3x + 5x + 7x = 15x . Given Perimeter = 300 m, so 15x = 300 ⇒ x = 20 . Th…