Question : What will be the area of a plot of quadrilateral shape, one of whose diagonals is 20 m and lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively?
Option 1: 400 m2
Option 2: 250 m2
Option 3: 200 m2
Option 4: 300 m2
Correct Answer: 300 m2
Solution : Given: The diagonals are 20 m and the lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively. Use the formula, $\text{Area of the triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}$. The area of the $\triangle ABC=\frac{1}{2}\times \text{AC}\times \text{BO}=\frac{1}{2} \times 20\times 12=120$ m2. The area of the $\triangle ADC=\frac{1}{2}\times \text{AC}\times \text{DP}=\frac{1}{2}\times 20\times 18=180$ m2. The area of a plot of quadrilateral shape = 180 + 120 = 300 m2 Hence, the correct answer is 300 m2.
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Question : The diagonal of a quadrilateral-shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. The area of the field is:
Option 1: 252 m2
Option 2: 156 m2
Option 3: 96 m2
Option 4: 1152 m2
Question : A field is in the shape of a trapezium whose parallel sides are 200 m and 400 m long, whereas each of the other two sides is 260 m long. What is the area (in m2) of the field?
Option 1: 72000
Option 2: 52000
Option 3: 48000
Option 4: 60000
Question : The curved surface area of a cone whose base radius is 7 cm and slant height is 10 cm is:
Option 1: 280 cm2
Option 2: 250 cm2
Option 3: 300 cm2
Option 4: 220 cm2
Question : A hall of 10 m in length, 5 m in width, and 6 m in height is to be painted (one side only). Determine the total surface area to be painted. (neglect the area of windows and doors)(floor area is NOT to be painted)
Option 1: 300 m2
Option 2: 280 m2
Option 3: 330 m2
Option 4: 230 m2
Question : The length of cold storage is 5 times its breadth, and its height is 8 m. The area of its four walls (including the doors) is 720 m2. Find the total surface area of cold storage.
Option 1: 1290.6 m2
Option 2: 1275.3 m2
Option 3: 1265.25 m2
Option 4: 1282.5 m2
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