CBSE Class 6 Mathematics Mensuration Assignment Set 07

Question. Find the perimeter of a \(\Delta\) Whose three sides are \(5\text{ cm}\), \(6\text{ cm}\) and \(7\text{ cm}\) resp.
Answer: Perimeter of a triangle = Sum of all three sides = \(5\text{ cm} + 6\text{ cm} + 7\text{ cm} = 18\text{ cm}\).

Question. Find the perimeter of an equilateral triangle whose each side is \(5\text{ cm}\)
Answer: Perimeter of an equilateral triangle = \(3 \times \text{side} = 3 \times 5\text{ cm} = 15\text{ cm}\).

Question. Find the perimeter of right angled triangle whose two legs are \(3\text{ cm}\) and \(4\text{ cm}\) and hypotenuse is \(5\text{ cm}\).
Answer: Perimeter of right angled triangle = Sum of three sides = \(3\text{ cm} + 4\text{ cm} + 5\text{ cm} = 12\text{ cm}\).

Question. Find the perimeter of an isosceles \(\Delta\) Whose one of the two equal side is \(5\text{ cm}\) and third side is \(6\text{ cm}\).
Answer: Perimeter of an isosceles triangle = Sum of sides = \(5\text{ cm} + 5\text{ cm} + 6\text{ cm} = 16\text{ cm}\).

Question. Find the side of an equilateral triangle if its perimeter is \(30\text{ cm}\)
Answer: Side of the equilateral triangle = \(\frac{\text{Perimeter}}{3} = \frac{30\text{ cm}}{3} = 10\text{ cm}\).

Question. Find the area of a triangle whose base is \(5\text{ cm}\) and altitude is \(4.5\text{ cm}\).
Answer: Area of the triangle = \(\frac{1}{2} \times \text{base} \times \text{altitude} = \frac{1}{2} \times 5\text{ cm} \times 4.5\text{ cm} = 11.25\text{ cm}^2\).

Question. Find the area of a right angled triangle whose two legs are \(4\text{ cm}\) and \(5\text{ cm}\) respectively and hypotenuse is \(\sqrt{41}\text{ cm}\).
Answer: Area of the right-angled triangle = \(\frac{1}{2} \times \text{product of the two legs} = \frac{1}{2} \times 4\text{ cm} \times 5\text{ cm} = 10\text{ cm}^2\).

Question. Find the side of an equilateral \(\Delta\) Whose area is \(4\sqrt{3}\text{ cm}^2\).
Answer: Area of an equilateral triangle = \(\frac{\sqrt{3}}{4} \times \text{side}^2\)
\(4\sqrt{3}\text{ cm}^2 = \frac{\sqrt{3}}{4} \times \text{side}^2\)
\(\text{side}^2 = 16 \implies \text{side} = 4\text{ cm}\).

Question. Find the area and perimeter of a square whose each side is \(4\text{ cm}\).
Answer: Area of the square = \(\text{side}^2 = 4\text{ cm} \times 4\text{ cm} = 16\text{ cm}^2\)
Perimeter of the square = \(4 \times \text{side} = 4 \times 4\text{ cm} = 16\text{ cm}\).

Question. If the area of a square is \(36\text{ cm}^2\), then find its perimeter.
Answer: Area of the square = \(\text{side}^2 = 36\text{ cm}^2 \implies \text{side} = 6\text{ cm}\)
Perimeter of the square = \(4 \times \text{side} = 4 \times 6\text{ cm} = 24\text{ cm}\).

Question. If the perimeter of a square is \(64\text{ cm}\), then find its area.
Answer: Perimeter of the square = \(4 \times \text{side} = 64\text{ cm} \implies \text{side} = 16\text{ cm}\)
Area of the square = \(\text{side}^2 = 16\text{ cm} \times 16\text{ cm} = 256\text{ cm}^2\).

Question. Find the perimeter of a rectangle whose length is \(40\text{ cm}\) and width is \(30\text{ cm}\).
Answer: Perimeter of the rectangle = \(2 \times (\text{length} + \text{width}) = 2 \times (40\text{ cm} + 30\text{ cm}) = 140\text{ cm}\).

Question. Find the area of a rectangle whose sides are \(13\text{ cm}\) and \(12\text{ cm}\).
Answer: Area of the rectangle = \(\text{length} \times \text{width} = 13\text{ cm} \times 12\text{ cm} = 156\text{ cm}^2\).

Question. If area of a rectangle is \(600\text{ m}^2\), and length is \(30\text{ m}\). Find its width.
Answer: Area of the rectangle = \(\text{length} \times \text{width}\)
\(600\text{ m}^2 = 30\text{ m} \times \text{width} \implies \text{width} = \frac{600\text{ m}^2}{30\text{ m}} = 20\text{ m}\).

Question. If perimeter of a rectangle is \(120\text{ cm}\) and the width is \(25\text{ cm}\). Find its length.
Answer: Perimeter of the rectangle = \(2 \times (\text{length} + \text{width})\)
\(120\text{ cm} = 2 \times (\text{length} + 25\text{ cm})\)
\(60\text{ cm} = \text{length} + 25\text{ cm} \implies \text{length} = 35\text{ cm}\).