For example, if you have a square and the length of one side is 4m{\displaystyle 4m}, you would multiply 4∗4{\displaystyle 44} to get 16m2{\displaystyle 16m^{2}}. Try it with a square that has sides 2in{\displaystyle 2in} long. Just multiply 2∗2{\displaystyle 22}. That square has an area of 4in2{\displaystyle 4in^{2}}. No matter what the unit is, it’s always squared when you’re talking about the area.
For example, if your rectangle has a length of 8m{\displaystyle 8m} and a width of 2m{\displaystyle 2m}, your equation would be A=8∗2{\displaystyle A=82}, which gives you an answer of A=16m2{\displaystyle A=16m^{2}}. What if your rectangle has bigger numbers? The formula still works the same way. For example, a rectangle with a length of 1762km{\displaystyle 1762km} and a width of 288km{\displaystyle 288km} would have an area of A=1762∗288=507,456km2{\displaystyle A=1762288=507,456km^{2}}.
For example, say you have a parallelogram with a base length of 4m{\displaystyle 4m} and a height of 2m{\displaystyle 2m}. Plug your numbers into the equation A=bh{\displaystyle A=bh} to get A=4∗2{\displaystyle A=4*2}, then simplify to find an area of 8m2{\displaystyle 8m^{2}}. Remember: the height isn’t the same as the length of the side! It’s the straight-line distance between the top and bottom bases.
For example, say you’ve got a trapezoid with a bottom side of 5m{\displaystyle 5m}, a top side of 3m{\displaystyle 3m}, and a height of 6{\displaystyle 6}. Start by adding the length of the two bases: 5+3=8{\displaystyle 5+3=8}. Then, divide by 2{\displaystyle 2} to get the average length of the bases: 4{\displaystyle 4}. You’ve taken care of the first part of the formula! Now all you have to do is multiply the average length of the bases, 4{\displaystyle 4}, by the height, 6{\displaystyle 6}: 4∗6=24{\displaystyle 4*6=24}. The area of your trapezoid is 24m2{\displaystyle 24m^{2}}.
For example, say you have a rhombus with diagonals of 9m{\displaystyle 9m} and 4m{\displaystyle 4m}. You know that 9x4=36{\displaystyle 9x4=36}. Divide 36{\displaystyle 36} by 2{\displaystyle 2}. The area of your rhombus is 18m2{\displaystyle 18m^{2}}. What if the product of the diagonals is an odd number? No problem, just express your answer as a decimal. For example, a rhombus with diagonals of 3cm{\displaystyle 3cm} and 7cm{\displaystyle 7cm} has an area of A=(3∗7)2=212=10. 5cm2{\displaystyle A={\frac {(3*7)}{2}}={\frac {21}{2}}=10. 5cm^{2}}.
For example, say you have a kite with diagonals of 4m{\displaystyle 4m} and 12m{\displaystyle 12m}. Plug those values into the formula: A=(4∗12)2=482=24{\displaystyle A={\frac {(4*12)}{2}}={\frac {48}{2}}=24}. The area of your kite is 24m2{\displaystyle 24m^{2}}.
If you’re working on a homework problem, the diagonal line might already be drawn for you. In fact, if you have a quadrilateral with a diagonal line, that’s a pretty big clue that you’ll use triangles to find the area.
If you’re working a problem for homework and you’re not given any way to measure these values, you can’t use triangles to find the area of that quadrilateral.
For example, say you have a diagonal with a length of 4{\displaystyle 4} that forms 2 triangles that each have a height of 2{\displaystyle 2}. Your formula would be A=12(4)(2){\displaystyle A={\frac {1}{2}}(4)(2)}, which simplifies to A=12(8){\displaystyle A={\frac {1}{2}}(8)}. So your answer would be A=4{\displaystyle A=4}. In this example, both triangles have the same area since they both have the same base and height.
To return to the previous example, since each triangle has an area of 4{\displaystyle 4}, you would simply add 4+4{\displaystyle 4+4} to get 8{\displaystyle 8}. Area is always expressed in square units. If the measurements in your original problem were meters, your answer would be 8m2{\displaystyle 8m^{2}}.
