All Intermediate Geometry Resources
Example Questions
Example Question #561 : Intermediate Geometry
In ΔABC: a = 8, b = 13, c = 9.
Find the area of ΔABC (to the nearest tenth).
36.1
40.4
33.9
29.6
35.5
35.5
In order to determine the area of a non-right triangle, we can use Heron's formula:
Using the information from the question, we obtain:
Example Question #562 : Intermediate Geometry
In ΔABC: a = 16, b = 11, c = 19.
Find the area of ΔABC (to the nearest tenth).
78.8
85.2
75.5
87.9
80.1
87.9
In order to determine the area of a non-right triangle, we can use Heron's formula:
Using the information from the question, we obtain:
Example Question #3 : How To Find The Area Of An Acute / Obtuse Triangle
Find the height of a triangle if its base is long and its area is
.
The formula to find the area of a triangle is
Substitute in the given values for area and base to solve for the height, :
Example Question #4 : How To Find The Area Of An Acute / Obtuse Triangle
In terms of , what is the area of a triangle with a height of
and a base of
?
The formula to find the area of a triangle is
Substitute in the given values for the base and the height to find the area.
Example Question #1 : How To Find The Area Of An Acute / Obtuse Triangle
Find the area of the triangle below. Round to the nearest tenths place.
The formula used to find the area of the triangle is
Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the length of the adjacent side, the triangle's height, and we know the length of the hypotenuse of the smaller triangle formed by the height.
Remember that
Now, solve for the height.
Now you can find the area of the triangle:
Example Question #1 : How To Find The Area Of An Acute / Obtuse Triangle
Find the area of the triangle below. Round to the nearest tenths place.
The formula used to find the area of the triangle is
Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the length of the adjacent side—the triangle's height—and we know the length of the hypotenuse of the smaller triangle formed by the height.
Remember that
Now, solve for the height.
Now you can find the area.
Example Question #7 : How To Find The Area Of An Acute / Obtuse Triangle
Find the area of the triangle below. Round to the nearest tenths place.
The formula used to find the area of the triangle is
Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the length of the adjacent side, the triangle's height, and we know the length of the hypotenuse of the smaller triangle formed by the height.
Remember that
Now, solve for the height.
Now you can find the area.
Example Question #8 : How To Find The Area Of An Acute / Obtuse Triangle
Find the area of the triangle below. Round to the nearest tenths place.
The formula used to find the area of the triangle is
Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the length of the adjacent side—the triangle's height—and we know the length of the hypotenuse of the smaller triangle formed by the height.
Remember that
Now, solve for the height.
Now you can find the area.
Example Question #9 : How To Find The Area Of An Acute / Obtuse Triangle
Find the area of the triangle below. Round to the nearest tenths place.
The formula used to find the area of the triangle is
Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the length of the adjacent side—the triangle's height—and we know the length of the hypotenuse of the smaller triangle formed by the height.
Remember that
Now, solve for the height.
Now you can find the area.
Example Question #10 : How To Find The Area Of An Acute / Obtuse Triangle
Find the area of the triangle below. Round to the nearest tenths place.
The formula used to find the area of the triangle is
Now, we will need to use a trigonometric ratio to find the length of the height. Because of the angle given, we will need to use , because we are looking for the height of the triangle, which in this case is the side opposite to the known angle, and we also know the length of the hypotenuse of the smaller triangle formed by the height.
Remember that
Now, solve for the height.
Now you can find the area.
All Intermediate Geometry Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)