A right triangle has legs of 12 cm and 16 cm. (a) Find the hypotenuse using Pythagoras theorem. (b) Find the area of the triangle. (c) A parallelogram has base 20 cm and perpendicular height 8 cm. Find its area. (d) Find the area of a triangle with all three sides 10 cm, 10 cm, and 12 cm using Heron's Formula.

Question

Accepted Answer

(a) HYPOTENUSE: c² = a² + b² = 12² + 16² = 144 + 256 = 400. c = √400 = 20 cm. (b) TRIANGLE AREA: A = ½ × base × height = ½ × 12 × 16 = 96 cm². (c) PARALLELOGRAM AREA: A = base × HEIGHT = 20 × 8 = 160 cm². (Note: Height is perpendicular, not the slant side.) (d) HERON'S FORMULA for sides 10, 10, 12: Semi-perimeter s = (10+10+12)/2 = 32/2 = 16 cm. Area = √[s(s-a)(s-b)(s-c)] = √[16(16-10)(16-10)(16-12)] = √[16 × 6 × 6 × 4] = √[2304] = 48 cm².

Practice — Lines, Angles, Triangles, Congruence, Mensuration & Data

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