Question : The area of a field in the shape of a hexagon is $1944 \sqrt{3} \mathrm{~m}^2$. What will be the cost (in INR) of fencing it at the rate of 11.50 per metre?
Option 1: 2,785
Option 2: 2,484
Option 3: 3,200
Option 4: 2,256
Correct Answer: 2,484
Solution : Area of the hexagon field = 1944$\sqrt{3}$ m$^2$ The rate of fencing the area = 11.50 per metre Area of the regular hexagon is $3\sqrt{3} × (\frac{a^2}{2})$ and its perimeter is $6a$, where $a$ is the side of the regular hexagon. Cost of the fencing = $6a$ × rate per metre Substituting the values in the formula $3\sqrt{3} × (\frac{a^2}{2}) = 1944\sqrt{3}$ ⇒ $a$ = 36 m The perimeter of the hexagon = $6a$ = 6 × 36 = 216 m Cost of fencing = 216 × 11.50 = INR 2,484 $\therefore$ Cost of fencing field in a hexagon shape is INR 2,484. Hence, the correct answer is 2,484.
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Question : A field is in the form of a circle. The cost of fencing around it at INR 12 per metre is INR 2,640. What is the area (in m2) of the field? (Take $\pi=\frac{22}{7}$)
Option 1: 1,925 m2
Option 2: 3,850 m2
Option 3: 2,772 m2
Option 4: 5,544 m2
Question : Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.
Option 1: $4 \sqrt{2} \mathrm{~cm}^2$
Option 2: $7 \sqrt{2} \mathrm{~cm}^2$
Option 3: $5 \sqrt{2} \mathrm{~cm}^2$
Option 4: $6 \sqrt{2} \mathrm{~cm}^2$
Question : Find the area of triangle whose sides are 10 cm, 12 cm, and 18 cm.
Option 1: $22 \sqrt{2} \mathrm{~cm}^2$
Option 2: $30 \sqrt{2} \mathrm{~cm}^2$
Option 3: $28 \sqrt{2} \mathrm{~cm}^2$
Option 4: $40 \sqrt{2} \mathrm{~cm}^2$
Question : The sides of a triangular field are 120 m, 170 m and 250 m. The cost of levelling the field at the rate of INR 7.40/m2 is:
Option 1: INR 65,120
Option 2: INR 63,640
Option 3: INR 59,200
Option 4: INR 66,600
Question : The area of an equilateral triangle is $4 \sqrt{3} \mathrm{~cm}^2$. Find the side (in cm) of the triangle.
Option 1: $2$
Option 2: $4$
Option 3: $\sqrt{3}$
Option 4: $2 \sqrt{3}$
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