How do you find the area of a rhombus parallelogram and trapezoid?

Answer 1

Rhombus :

1. The "base times height" method First pick one side to be the base. Any one will do, they are all the same length. Then determine the altitude - the perpendicular distance from the chosen base to the opposite side. The area is the product of these two, or, as a formula: where

b is the length of the base

a is the altitude (height).

2. The "diagonals" method Another simple formula for the area of a rhombus when you know the lengths of the diagonals. The area is half the product of the diagonals. As a formula: where

d1 is the length of a diagonal

d2 is the length of the other diagonal

2. Using trigonometry If you are familiar with trigonometry, there is a handy formula when you know the length of a side and any angle: where

s is the length of any side

a is any interior angle

sin is the sine function (see Trigonometry Overview) It may seem odd at first that you can use any angle since they are not all equal. But the angles are either equal or supplementary, and supplementary angles have the same sine.

Parallelogram:

The area of a rectangle is given by the formula

where

B is the length of any base

A is the corresponding altitude Recall that any side can be chosen as the base. You must use the altitude that goes with the base you choose. The altitude (or height) of a parallelogram is the perpendicular distance from the base to the opposite side (which may have to be extended).

Trapezoid:

Area formula The area of a trapezoid is given by the formula

where

b1, b2 are the lengths of the two bases

a is the altitude of the trapezoid

Calculator Recall that the bases are the two parallel sides of the trapezoid. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases. This is equivalent to the altitude times the average length of the bases. Since the median of a trapezoid is also the average length of the two bases, the area is also the altitude times the median length. Area as a compound shape Another way to find the area of a trapezoid is to treat it as some simpler shapes, and then add or subtract their areas to find the result. For example, a trapezoid could be considered to be a smaller rectangle plus two right triangles: