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The area of a rectangle is calculated by multiplying its length by its width, expressed as $A = l \times w$.

Conditions: Applies specifically to rectangles.; Length and width are measured in the same linear unit.

The area of a rectangle is calculated by multiplying its length by its width, expressed as $A = l \times w$.

Conditions: Applies specifically to rectangles.; Length and width are measured in the same linear unit.

No, the order of addition does not matter. You get the correct perimeter regardless of the sequence in which you add the side lengths, because they are the same set of numbers being summed.

Conditions: The same set of side lengths is being summed.; Addition is ordinary real-number addition.

No, the order of addition does not matter. You get the correct perimeter regardless of the sequence in which you add the side lengths, because they are the same set of numbers being summed.

Conditions: The same set of side lengths is being summed.; Addition is ordinary real-number addition.

To calculate the perimeter of a rectangle, add the lengths of all four of its sides. For the rectangle shown, the side lengths are 2 ft, 6 ft, 2 ft, and 6 ft, giving the expression $P = 2 + 6 + 2 + 6$.

Conditions: Use all side lengths of the shape.; Units must be consistent; here all lengths are in feet.

To calculate the perimeter of a rectangle, add the lengths of all four of its sides. For the rectangle shown, the side lengths are 2 ft, 6 ft, 2 ft, and 6 ft, giving the expression $P = 2 + 6 + 2 + 6$.

Conditions: Use all side lengths of the shape.; Units must be consistent; here all lengths are in feet.

The trapezoidal rule approximates an integral by replacing the curve over an interval with a straight line between two sampled points and computing the area of the resulting trapezoid. In composite form, the endpoint values are each weighted by one half because interior points belong to two neighboring trapezoids, while endpoints belong to only one.

Conditions: Applied to numerical integration over an interval [a,b].; Uses function values at the interval endpoints.; For composite use, adjacent subinterval endpoints are shared, producing half weights at the outer endpoints.

The trapezoidal rule approximates an integral by replacing the curve over an interval with a straight line between two sampled points and computing the area of the resulting trapezoid. In composite form, the endpoint values are each weighted by one half because interior points belong to two neighboring trapezoids, while endpoints belong to only one.

Conditions: Applied to numerical integration over an interval [a,b].; Uses function values at the interval endpoints.; For composite use, adjacent subinterval endpoints are shared, producing half weights at the outer endpoints.

By placing strips of height $2\pi r$ along the radius axis, their tops form a linear graph. As the partition width goes to zero, the step-function approximation converges to the area under the line $y=2\pi x$.

Conditions: Function $f(r) = 2\pi r$ is linear; Partition width $\Delta r \to 0$

By placing strips of height $2\pi r$ along the radius axis, their tops form a linear graph. As the partition width goes to zero, the step-function approximation converges to the area under the line $y=2\pi x$.

Conditions: Function $f(r) = 2\pi r$ is linear; Partition width $\Delta r \to 0$