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parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long then its area is:__________?

Correct answer: C. 600√15 sq.m

  • A. 480 sq.m
  • B. 320 sq.m
  • C. 600√15 sq.m
  • D. 450√15

Explanation

For the diagonal of 80 metres, the cosine rule gives 80² = 60² + 40² − 2 × 60 × 40 cos θ, so cos θ = 1/4. Thus sin θ = √(1 − 1/16) = √15/4, and the parallelogram area is 60 metres × 40 metres × √15/4 = 600√15 square metres. The likely mistake is choosing 480 square metres by multiplying the side lengths without including the angle between them.

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Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.

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