Question : The sides of a triangle are 6 cm, 8 cm, and 10 cm. What is the area of the triangle?
Option 1: 20 cm2
Option 2: 28 cm2
Option 3: 24 cm2
Option 4: 16 cm2
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Correct Answer: 24 cm2
Solution : Given: Sides of the triangle = 6 cm, 8 cm, and 10 cm. Using Heron's formula the area of a triangle, $A = \sqrt{s(s-a)(s-b)(s-c)}$ Where $s$ is the semi-perimeter of the triangle, which is half the perimeter of the triangle, and $a,b,c$ are the sides of the triangle. The perimeter of the triangle is the sum of the lengths of its sides, which is: $P = a + b + c$ Semiperimeter = $s = \frac{a+b+c}{2}$ $s = \frac{6+8+10}{2} = 12$ $A = \sqrt{12(12-6)(12-8)(12-10)}$ $ = \sqrt{12 \times 6 \times 4 \times 2}$ $ = \sqrt{576}$ $ = 24$ Hence, the correct answer is 24 cm2.
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Question : The sides of a triangle are 20 cm, 48 cm, and 52 cm. What is the area of the triangle?
Option 1: 320 cm2
Option 2: 480 cm2
Option 3: 560 cm2
Option 4: 245 cm2
Question : The ratio of the sides of a triangle is 3 : 3 : 4. If the area of a triangle is $32 \sqrt{5}$ cm2, then what is the length of the equal sides?
Option 1: 12 cm
Option 2: 16 cm
Option 3: 10 cm
Option 4: 15 cm
Question : Find the area of the rhombus whose diagonals are 16 cm and 20 cm.
Option 1: 110 cm2
Option 2: 150 cm2
Option 3: 160 cm2
Option 4: 120 cm2
Question : What will be the volume of a sphere with a radius of 65 cm? (approximately)
Option 1: $4.5 \times 10^6 $ cm3
Option 2: $6 \times 10^6$ cm3
Option 3: $1.15 \times 10^6$ cm3
Option 4: $2 \times 10^6$ cm3
Question : A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. The area of the parallelogram is:
Option 1: 42 cm2
Option 2: 60 cm2
Option 3: 84 cm2
Option 4: 96 cm2
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