Area: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 8)

Let the sides be a = 26 cm, b = 28 cm, c = 30 cm. Semi-perimeter s = (a+b+c)/2 = (26+28+30)/2 = 42. s-a = 16, s-b = 14, s-c = 12. Heron’s formula: Area = sqrt[s(s-a)(s-b)(s-c)]. Product under the root = 42 x 16 x 14 x 12 = 112896. Area = sqrt(112896) = 336 sq cm.

Let base = b = 5 cm and height = h = 42 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 5 x 42 = 105 sq cm.

Let base = b = 18 cm and height = h = 29 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 18 x 29 = 261 sq cm.

Let base = b = 37 cm and height = h = 6 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 37 x 6 = 111 sq cm.

Let base = b = 37 cm and height = h = 34 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 37 x 34 = 629 sq cm.

Let base = b = 34 cm and height = h = 14 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 34 x 14 = 238 sq cm.

Let base = b = 26 cm and height = h = 8 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 26 x 8 = 104 sq cm.

Let base = b = 7 cm and height = h = 16 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 7 x 16 = 56 sq cm.

Let base = b = 13 cm and height = h = 48 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 13 x 48 = 312 sq cm.

Let base = b = 16 cm and height = h = 44 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 16 x 44 = 352 sq cm.

Let base = b = 46 cm and height = h = 15 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 46 x 15 = 345 sq cm.

Let base = b = 40 cm and height = h = 17 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 40 x 17 = 340 sq cm.

Let base = b = 23 cm and height = h = 38 cm. Area of a triangle = (1/2) x b x h. So area = (1/2) x 23 x 38 = 437 sq cm.

Let length = L = 27 m and breadth = B = 120 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 27^2 = 729. B^2 = 120^2 = 14400. diagonal^2 = 729 + 14400 = 15129. diagonal = sqrt(15129) = 123 m.

Let length = L = 21 m and breadth = B = 72 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 21^2 = 441. B^2 = 72^2 = 5184. diagonal^2 = 441 + 5184 = 5625. diagonal = sqrt(5625) = 75 m.

Let length = L = 18 m and breadth = B = 24 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 18^2 = 324. B^2 = 24^2 = 576. diagonal^2 = 324 + 576 = 900. diagonal = sqrt(900) = 30 m.

Let length = L = 21 m and breadth = B = 28 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 21^2 = 441. B^2 = 28^2 = 784. diagonal^2 = 441 + 784 = 1225. diagonal = sqrt(1225) = 35 m.

Let length = L = 16 m and breadth = B = 30 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 16^2 = 256. B^2 = 30^2 = 900. diagonal^2 = 256 + 900 = 1156. diagonal = sqrt(1156) = 34 m.

Let length = L = 24 m and breadth = B = 70 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 24^2 = 576. B^2 = 70^2 = 4900. diagonal^2 = 576 + 4900 = 5476. diagonal = sqrt(5476) = 74 m.

Let length = L = 6 m and breadth = B = 8 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 6^2 = 36. B^2 = 8^2 = 64. diagonal^2 = 36 + 64 = 100. diagonal = sqrt(100) = 10 m.

Let length = L = 5 m and breadth = B = 12 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 5^2 = 25. B^2 = 12^2 = 144. diagonal^2 = 25 + 144 = 169. diagonal = sqrt(169) = 13 m.

Let length = L = 7 m and breadth = B = 24 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 7^2 = 49. B^2 = 24^2 = 576. diagonal^2 = 49 + 576 = 625. diagonal = sqrt(625) = 25 m.

Let length = L = 12 m and breadth = B = 35 m. The line between opposite corners is the diagonal. It splits the rectangle into two right triangles, so by the Pythagorean theorem, diagonal^2 = L^2 + B^2. L^2 = 12^2 = 144. B^2 = 35^2 = 1225. diagonal^2 = 144 + 1225 = 1369. diagonal = sqrt(1369) = 37 m.

Let diagonal = D = 52 m. Area of a square in terms of its diagonal is D^2/2. So area = 52^2/2 = 2704/2 = 1352 sq m.

Let diagonal = D = 10 m. Area of a square in terms of its diagonal is D^2/2. So area = 10^2/2 = 100/2 = 50 sq m.