How to calculate the area of a triangle using trigonometry?
Throughout geometry studies, which deal with various structures and shapes, you are required to calculate areas and perimeters. As known, each shape or structure has a different formula through which you can answer the question and calculate the area. Fortunately, there is one formula that you can use for all triangles, and it can answer the question of how to calculate the area of a triangle using trigonometry?
In mathematics studies, emphasis is also placed on trigonometry, which deals with the study of triangles, their angles, and sides. Every student is required to demonstrate knowledge of triangles (from right triangles to isosceles triangles), and thus also answer the question of how to calculate the area of a triangle using trigonometry.
One formula for all different triangles
Now that you know the formula for calculating the area of a triangle using trigonometry, you can use it in any question where you need to calculate areas in triangles. The formula for calculating the triangle:
Due to the fact that AB is perpendicular to BC and forms a 90-degree angle,
it can be argued that AB is the height of the triangle.
Hence we can calculate the area as follows:
2AB×BC=28×6=248=24
Answer
24 cm²
Exercise #2
Calculate the area of the triangle ABC using the data in the figure.
Video Solution
Step-by-Step Solution
First, let's remember the formula for the area of a triangle:
(the side * the height that descends to the side) /2
In the question, we have three pieces of data, but one of them is redundant!
We only have one height, the line that forms a 90-degree angle - AD,
The side to which the height descends is CB,
Therefore, we can use them in our calculation:
2CB×AD
28×9=272=36
Answer
36 cm²
Exercise #3
What is the area of the triangle in the drawing?
Video Solution
Step-by-Step Solution
First, we will identify the data points we need to be able to find the area of the triangle.
the formula for the area of the triangle: height*opposite side / 2
Since it is a right triangle, we know that the straight sides are actually also the heights between each other, that is, the side that measures 5 and the side that measures 7.
We multiply the legs and divide by 2
25×7=235=17.5
Answer
17.5
Exercise #4
Calculate the area of the following triangle:
Video Solution
Step-by-Step Solution
The formula for calculating the area of a triangle is:
(the side * the height from the side down to the base) /2
That is:
2BC×AE
We insert the existing data as shown below:
24×5=220=10
Answer
10
Exercise #5
Calculate the area of the following triangle:
Video Solution
Step-by-Step Solution
The formula for the area of a triangle is
A=2h⋅base
Let's insert the available data into the formula:
(7*6)/2 =
42/2 =
21
Answer
21
Question 1
Calculate the area of the triangle below, if possible.