How to Find Area

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Finding the area of various geometric figures is a simple and useful mathematical operation that often proves useful in the real world. Finding the area of square or rectangular figures is quite simple. Calculating the area of circles, triangles or other figures can be a bit trickier.

    Calculate the area of a square by squaring the length of one of the sides. In other words, if the length of a side of a square is X, then the area (denoted by the letter A) of the square is X^2. Therefore, A = X^2 for squares.

    Know that rectangles have two short sides and two long sides. The length (L) denotes the long side of the figure, and the width (W) denotes the short side. To find the area of a rectangle, multiply the length by the width. Therefore, A = L x W for rectangles.

    Find the area of a triangle. The base of the triangle (B) is on the bottom, and the height (H) is defined as the length of a straight line dropped from the tip of the triangle down to its base. To calculate the area of a triangle, multiply the base by the height by 1/2. In other words, A = (1/2) B x H for triangles.

    Use a calculator to figure the area of a circle. Here, you are working with a constant. To find the area of a circle, you must first find the radius (R), which is equal to 1/2 of the diameter--a line that cuts a circle equally in half. To find the area, multiply the constant pi (a good approximation for this value is 3.14) by the radius squared. So, A = 3.14 x R^2 for circles.

    Know that a trapezoid is a four-sided figure with a set of parallel sides. Though it might seem impossible to calculate the area of trapezoids, there is a formula that will help you make sense of it all. Simply add the values of both bases (hint: these are the parallel sides) and divide this number by 2. Multiply this number by the height of the trapezoid. In other words, A = (B1 + B2 / 2) x H for any trapezoid.

    Tips

    • Depending on the type of figure, you may need to make a few measurements before making a calculation. If you are solving a math problem in a textbook, the necessary measurements have likely been made for you already. If you are working with real-world figures, such as your rectangular living room floor, find the length, width, base, height and/or diameter measurements with a ruler or tape measure.

    Warnings

    • Always check your work (even if you are using a calculator), particularly if you are using these measurements to calculate how much of something you will need to buy or order, such as carpet or hardwood flooring. A few extra seconds checking your work can save from a mistake that costs you money and time.

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