The formula for the area of a triangle is one-half times the base times the height.
If your triangle has a base of 12 feet and two other sides each at 7 feet. The height is unknown. Drop a line down from the point of the triangle to the base. This divides the triangle into two equal halves which each are right triangles. The formula for the sides of a right triangle are the Pythagorean theorem that states A-squared plus B-squared equals C-squared where "C" is the hypotneuse or the side opposite the right angle, and A and B are the remaining two sides. In your case, you know C, the hypotneuse, is 7 and B, the base is 6 or one-half of 12 (since you divided the triangle into two parts). The formula then is reworked to read C-squared minus B-squared equals A-squared. In numerals that is 7-squared or 49 minus 6-squared or 36. The answer of 13 is A-squared and the square root of 13 is 3.6. that number is the height of the right triangle.
So now to apply the area formula of one-half times base times height. The base is 6, height is 3.6 which multiplied equals 21.6 and half of that is 10.8. Remember that you have two parts of the original triangle. The second part has the same area as the first, or another 10.8. Putting the two together gives you 21.6 square feet.
The method and formula also work when all sides of the triangle are unequal. Say that you triangle has a 12 foot base and was 7 feet on one side but only 6 feet on the other. You would need to do some actual measurements or scale the measurements to figure out the answer. When you drop a line from the upper point of the triangle to the base, in the case of unequal sides the line would not split the base exactly in half and one portion of the base would be longer than the other. Once you determine the measurements along the base line then follow the same method and formula to get the answers.
This method works better if you do not know the height, or do not feel like figuring the height.
First figure up the perimeter of the triangle. This example we will use a triangle with side A 15 inches, side B 10 inches, and side C 7 inches.
Perimeter equals A plus B plus C P=15+10+7 P=32
Now for the area
Area equals the square route of the perimeter divided by 2 times the perimeter divided by 2 minus side A times the perimeter divided by 2 minus side B times the perimeter divided by 2 minus side c
A=sqt((32/2)((32/2)-15)((32/2)-10)((32/2)-7)) A=sqt(16(16-15)(16-10)(16-7)) A=sqt(16*1*6*9) A=sqt(864) A=29.39 square inches.