Question : Each side of a square is 12 cm long. The perimeter of this square is equal to the perimeter of a rectangle whose length is 16 cm. What will be the area of this rectangle?
Option 1: 128 cm2
Option 2: 112 cm2
Option 3: 184 cm2
Option 4: 156 cm2
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Correct Answer: 128 cm2
Solution : The side of a square = 12 cm Length of the rectangle = 16 cm Perimeter of the square = 4 × side = 4 × 12 = 48 cm The perimeter of a rectangle = 48 cm (since it is equal to the perimeter of the square) Let's assume the width of the rectangle to be 'w'. Perimeter of rectangle = 2 × (length + width) ⇒ 48 = 2 × (16 + w) ⇒ 24 = 16 + w $\therefore$ w = 24 – 16 = 8 Therefore, the width of the rectangle is 8 cm. The area of the rectangle can be calculated as: Area of rectangle = length × width = 16 × 8 = 128 cm2 Hence, the correct answer is 128 cm2.
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Question : The length of each side of a square is 16 cm. What is the area of the square?
Option 1: 112 cm2
Option 2: 176 cm2
Option 3: 128 cm2
Option 4: 256 cm2
Question : The length of each side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then what is the area of the rhombus?
Option 1: 108 cm2
Option 4: 96 cm2
Question : The breadth of a rectangle is $\frac{4}{5}$th of the radius of a circle. The radius of the circle is $\frac{1}{5}$ of the side of a square, whose area is 625 cm2. What is the area of the rectangle if the length of the rectangle is 20 cm?
Option 1: 150 cm2
Option 2: 600 cm2
Option 3: 100 cm2
Option 4: 80 cm2
Question : The total surface area of a closed cube is 128 cm2 more than the area of a square. If the length of each side of the cube is 8 cm, then what is the length of each side of the square?
Option 1: 16 cm
Option 2: 12 cm
Option 3: 18 cm
Option 4: 9 cm
Question : 5 times the perimeter of a square is 600 cm. What will be the area of this square?
Option 1: 900 cm2
Option 2: 1150 cm2
Option 3: 750 cm2
Option 4: 480 cm2
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