Area Formulas Use the same units for all measurements. The area of a figure is the number of squares required to cover it completely, like tiles on a floor. Geometry Formulas. Areas and Perimeters. Figure. Sketch. Area. Perimeter. Square. A = s. 2. P = 4s. Rectangle. A = lw. P = 2l + 2w. Parallelogram. A = lh. Area and Volume Formula for geometrical figures - square, rectangle, triangle, polygon, circle, ellipse, trapezoid, cube, sphere, cylinder and cone.

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### Area Formulas for Geometric Figures.

Area of trapezoid Doubling the trapezoid and then halving the resulting area As was true with the triangle, two copies of a trapezoid can be fit together to make a parallelogram. The height of all area formulas parallelogram is the same as the height of the trapezoid, but its base is the sum of the two bases of the all area formulas.

But that area is two trapezoids, so we need to all area formulas it in half to get the area of the trapezoid. Dissecting the trapezoid We could also dissect the trapezoid the way we dissected the triangle, with a single slice cutting its height in half.

The two parts fit together to make a parallelogram whose base is the sum of the two bases of the trapezoid, but whose height is half the height of the trapezoid.

In the case of the trapezoid, the bases cannot be chosen at will. The two parallel sides are the bases, and height, as always, is the all area formulas distance from one base to the opposite. Because the parallelogram is made from exactly the all area formulas "stuff" as the trapezoid, that's the area of the trapezoid, too.

Area of other special quadrilaterals Area of rhombus The area of a rhombus can be found by cutting and rearranging the pieces to form a parallelogram.

All area formulas can be done several ways: Cut across the shorter diagonal a to form two congruent triangles. Move the lower half of the triangle next to the upper half to form a parallelogram.

The shorter diagonal a becomes the base of the parallelogram, and half the longer diagonal b becomes the height of the parallelogram. Another all area formulas way is to cut the rhombus into four congruent triangles and rearranging them into a rectangle with the shorter diagonal as the base and half the longer diagonal as the height.

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Then multiply by two since there are two of them: Cutting across the all area formulas diagonal yields two congruent triangles. If we rearrange them, we can form a parallelogram with the longer diagonal b as base and half the shorter diagonal a as the height.

A more complicated approach involve a bit of algebra. Cut the kite all area formulas the shorter diagonal to form two triangles with the shorter diagonal a as the base.

Well, what do you know.

## Measurement: Discovering formulas for area | Think Math!

Basically, you only need to know the formula for the area of a parallelogram and then derive the formula for the others.

What about, say… the circle?

First, slice your circle up like a pizza. Then, rearrange the slices in an alternating pattern, to get a shape like this: It looks kind of like a parallelogram, right? Notice that this base is half the all area formulas. Now, slice it up even finer, and repeat the process.