Area of Triangles: Using Base and Height
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If the rectangle is cut in half, we know have a triangle. So the area would be half the area of the rectangle.
![](/math/geometry/topics/images/area_of_triangles-_part1_image2.jpg)
Let's use the formula in some examples.
Ex. 1) Calculate the area of the triangle.
![](/math/geometry/topics/images/area_of_triangles-_part1_image3.png)
Ex. 2) Calculate the area of the triangle.
![](/math/geometry/topics/images/area_of_triangles-_part1_image4.png)
Ex. 3) Determine the area of the triangle.
![](/math/geometry/topics/images/area_of_triangles-_part1_image5.png)
Ex. 4) The area of the triangle is 32 cm2. Determine the height.
![](/math/geometry/topics/images/area_of_triangles-_part1_image6.jpg)
To help visualize what this problem is asking, draw the other half so that it forms a rectangle.
![](/math/geometry/topics/images/area_of_triangles-_part1_image7.jpg)
This rectangle would have an area of 64 cm2.
A = bh
64 = 10(x)
![](/math/geometry/topics/images/area_of_triangles-_part1_image8.png)
x = 6.4 cm
A = bh
64 = 10(x)
![](/math/geometry/topics/images/area_of_triangles-_part1_image8.png)
x = 6.4 cm
Let's review the steps.
Step 1: Double the area of the triangle. (This "undoes" the dividing by 2.)
Step 2: Divide the new area by the given side length.
Step 1: Double the area of the triangle. (This "undoes" the dividing by 2.)
Step 2: Divide the new area by the given side length.
![](/math/geometry/topics/images/area_of_triangles-_part1_image9.png)
Ex. 5) The area of the triangle is 40 in2. Determine the length of the height.
![](/math/geometry/topics/images/area_of_triangles-_part1_image10.jpg)
Solution:
Remember, double the area and then divide by the known side length.
![](/math/geometry/topics/images/area_of_triangles-_part1_image15.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image11.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image12.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image13.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image16.png)
Remember, double the area and then divide by the known side length.
![](/math/geometry/topics/images/area_of_triangles-_part1_image15.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image11.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image12.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image13.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image14.png)
![](/math/geometry/topics/images/area_of_triangles-_part1_image16.png)
Let's Review
To calculate the area of a triangle, we multiply the base times the height and divide by 2. If you are given the area, follow the steps backwards. You will multiply by 2 and divide by the given length.
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