Area of a circle = πr². Using π ≈ 3.14, Area = 3.14 × (7)² = 3.14 × 49 = 153.86 cm², which rounds to 154 cm².

Volume = (1/3)πr²h = (1/3) * 3.14 * (4)² * 9 = 113.04 cm³.

Let the width be x units. Then the length is 2x units. Area = length × width = 2x * x = 2x^2. Setting this equal to 200 gives 2x^2 = 200, so x^2 = 100, and x = 10 units.

Area = length × width. Thus, 48 = 12 × width, giving width = 48/12 = 4 meters.

Area of the garden = 10 * 6 = 60 m². Area including the path = (10 + 2) * (6 + 2) = 12 * 8 = 96 m². Area of the path = 96 - 60 = 36 m².

Perimeter of a square = 4 × side. Thus, 40 = 4 × side, giving side = 10 cm. Area = side² = 10² = 100 cm².

Area = (1/2) * (base1 + base2) * height = (1/2) * (10 + 6) * 4 = 32 cm².

Area of a trapezium = (1/2) × (base1 + base2) × height = (1/2) × (10 + 6) × 4 = 32 cm².

The triangle is a right triangle (7² + 24² = 25²). The area is (1/2) * base * height = (1/2) * 7 * 24 = 84 cm².

The equation of the circle is x² + y² = 25. The point (6, 0) gives 6² + 0² = 36, which is greater than 25, hence it lies outside.

To find the y-intercept, set x = 0. The equation becomes -4y = 12, thus y = -3. The y-intercept is (0, -3).

The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.

The sum of the interior angles of an octagon (8-sided polygon) is calculated using the formula (n-2) * 180, which gives (8-2) * 180 = 1080 degrees.

A quadrilateral with one pair of parallel sides is classified as a trapezium.

Supplementary angles sum up to 180 degrees. Therefore, angle B = 180 - 45 = 135 degrees.

Let the angles be 2x, 3x, and 4x. The sum of angles in a triangle is 180 degrees. Therefore, 2x + 3x + 4x = 180. Solving gives x = 20, so the largest angle is 4x = 80 degrees.

Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 units.

In the formula for the area of a quadrilateral, d1 and d2 represent the lengths of the diagonals.

Area of a sector = (θ/360) × πr². Thus, 30 = (θ/360) × π × 25. Solving gives θ = (30 × 360)/(25π) ≈ 72°.

Area of a square = side². Therefore, side = √64 = 8 cm.

The area of a triangle is given by the formula Area = 1/2 * base * height. Thus, 24 = 1/2 * 8 * height, which gives height = 6 cm.

Area of a triangle = (1/2) × base × height. Thus, 50 = (1/2) × 10 × height. Solving gives height = 10 units.

Circumference = 2πr. Therefore, r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Using the formula C = 2πr, we find r = C/(2π) = 31.4/(2*3.14) = 5 cm.

If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.

To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, leading to y = 2.

'm' in the equation of a line represents the slope, which indicates the steepness and direction of the line.

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides can be calculated as 360 / 30 = 12.

The area of a rhombus can be calculated using the formula (1/2) × d1 × d2 = (1/2) × 10 × 24 = 120 cm².

Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.