THE area of triangle is the measure of its surface and uses as a unit of measure any measure of length squared, for example square meters, square centimeters etc. Generally speaking, the area of a triangle consists of half of the multiplication from base to height.
Read too: Circumference - flat figure consisting of the set of points equidistant from the center
How to calculate the area of a triangle?
The triangle is the polygon simpler than there is, but this does not diminish its importance, since it can be explored in several areas of mathematics and physics. Although there are a few different formulas for equilateral triangles and rectangles, calculating the area of any triangle basically needs to know the base (b) and height (h) values.
A→ area
b → base
h→ height
Example
Calculate the area of the triangle below:
Generally, this formula is efficient for calculating area of all triangles, like the scalene triangle, isosceles and equilateral.
right triangle area
the area of a right triangle
is very similar to the area of any triangle, but in this specific case, the height coincides with one of its sides, therefore, the base and height coincide with the legs (the smaller sides) of the right triangle. Only in the right triangle is it possible to calculate the area value multiplying the perpendicular sides. Let a and b be the legs, as in the image below, it is possible to calculate the area from the multiplication of the legs divided by 2.
Example
A right triangle has sides measuring 6 cm, 8 cm and 10 cm. What is the area of this triangle?
To calculate the area of the triangle, we need to identify the two sides. The hypotenuse of a right triangle is always the longest side, so it measures 10 cm. So, the collared pecs measure 6 cm and 8 cm.
See too: Cone – geometric solid formed from the rotation of a triangle
equilateral triangle area
It is known that the equilateral triangle It has all sides congruent, that is, they have the same measurement. The equilateral triangle is a special case of a triangle that has a specific formula for calculating the area. In an equilateral triangle, you can calculate its area knowing only the value of one side. This is because the equilateral triangle has all of its angles measuring 60°.
Example
Find the area of the equilateral triangle whose side measures 6 cm.
solved exercises
Question 1 - A land will be divided into three parts for the construction of a garden. The green area will be filled with grass, as shown in the following image:
Knowing that grass costs R$9.00 per square meter and that this rectangular region has sides measuring 14m and 6m, what will be the amount spent on grass?
A) BRL 399.00
B) BRL 400.00
C) BRL 798.00
D) BRL 800.00
Resolution
Alternative A
1st step: calculate the area of the triangle, knowing that the base measures 14 meters and the height measures 6 meters
2nd step: Calculate the amount spent
9,50 · 42 = 399,00
Question 2 - What is the approximate area of an equilateral triangle that has a side measuring 5 cm?
A) 41.9 cm²
B) 41.6 cm²
C) 20.9 cm²
D) 20.8 cm²
Resolution
Alternative D
Performing rounding, the closest area value is 20.8 cm² .
