Question : If the length of the side of an equilateral triangle is 8 cm, what is its area (in cm2)?
Option 1: $32\sqrt{3}$
Option 2: $16$
Option 3: $16\sqrt{3}$
Option 4: $32$
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Correct Answer: $16\sqrt{3}$
Solution : The area of an equilateral triangle with side length $a$, $= \frac{\sqrt{3}}{4}a^2$ On substituting $a$ = 8 cm, The area of an equilateral triangle $= \frac{\sqrt{3}}{4} \times 8^2 = 16\sqrt{3} \text{ cm}^2$ Hence, the correct answer is $16\sqrt{3}$.
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Question : The length of each side of an equilateral triangle is 22 cm. Find the area (in cm2) of this triangle.
Option 1: 121
Option 2: $242 \sqrt{3}$
Option 3: $121 \sqrt{3}$
Option 4: 242
Question : In an equilateral triangle STU, inradius is $5 \sqrt{3 }\mathrm{~cm}$. What is the length of the side of this equilateral triangle?
Option 1: $20 \sqrt{3} \mathrm{~cm}$
Option 2: $18 \sqrt{3} \mathrm{~cm}$
Option 3: $30 \mathrm{~cm}$
Option 4: $24 \mathrm{~cm}$
Question : In a triangle the length of the opposite side of the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?
Option 1: $8\sqrt{2}$ cm
Option 2: $4\sqrt{2}$ cm
Option 3: $8\sqrt{3}$ cm
Option 4: $4\sqrt{3}$ cm
Question : The length of the base of a triangle is 10 cm and its altitude from the same base is 8 cm. What is the area of the triangle?
Option 1: 30 cm2
Option 2: 40 cm2
Option 3: 50 cm2
Option 4: 80 cm2
Question : The sides of a triangle are of length 8 cm, 15 cm, and 17 cm. Find the area of the triangle.
Option 1: 65 cm2
Option 2: 75 cm2
Option 3: 60 cm2
Option 4: 70 cm2
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