Content

• To step
• Method 1 of 2: Pyramid with a rectangular base
• Method 2 of 2: Pyramid with a triangular base
• Tips
• Warnings

To calculate the volume of a pyramid, you must multiply the area of ​​the base by the height of the pyramid. You divide the result by 3, that's all! Read this article with calculation methods for a pyramid with a rectangular base and a pyramid with a triangular base.

To step

Method 1 of 2: Pyramid with a rectangular base

1. Determine the length and width of the base. In this example, the length is 4 cm and the width is 3 cm. If you have a square base, the method is the same, except the length and width are the same. Write down your measurements.
2. Multiply the length by the width to find the area of ​​the base. To calculate the area of ​​our example, we multiply 3 cm by 4 cm. 3 cm x 4 cm = 12 cm
3. Multiply the area of ​​the base by the height. The area of ​​the base is 12 cm and the height is 4 cm, so we multiply 12 cm by 4 cm. 12 cm x 4 cm = 48 cm
4. Divide the result by 3. That's the same as multiplying by 1/3. 48 cm / 3 = 16 cm. The volume of a pyramid with a height of 4 cm and a rectangular base with a width of 3 cm and a length of 4 cm is therefore 16 cm. Do not forget to state the result in cubic units.

Method 2 of 2: Pyramid with a triangular base

1. Determine the length and width of the base. The length and width of the base should perpendicular to each other, otherwise this method will not work. They can also be thought of as the bottom and the height of the triangle. In this example, the width of the triangle is 2 cm and the length is 4 cm. Write this down.
2. Calculate the area of ​​the ground plane. To calculate the area of ​​the base, we use the following formula:A = 1/2 (o) (h). This is how we do it:
   • A = 1/2 (o) (h)
   • A = 1/2 (2) (4)
   • A = 1/2 (8)
   • A = 4 cm
3. Multiply the area of ​​the base by the height of the pyramid. The area of ​​the base is 4 cm and the height is 5 cm. 4 cm x 5 cm = 20 cm.
4. Divide the result by 3. 20 cm / 3 = 6.67 cm. The volume of a pyramid with a height of 5 cm and a triangular base with a width of 2 cm and a length of 4 cm is therefore 6.67 cm.

Tips

• In a pyramid with a square base, the height, the line that divides the triangular side face into two equal triangles, and the width of the base connected by the Pythagorean theorem are: (width ÷ 2) + (height) = (height of triangle)
• This method can also be applied to objects such as pentagonal pyramids, hexagonal pyramids, etc. The general process is: A) calculate the area of ​​the base; B) Measure the height from the top of the pyramid to the center of the base; C) multiply A by B; D) divide by 3.
• In all ordinary pyramids are the upright ribs, the line that divides the triangular side face into two equal triangles and the width of the base connected by the Pythagorean theorem: (length of the side ÷ 2) + (length of rib) = (height)

Warnings

• Pyramids have three types of heights: the line that divides the triangular side face into two equal triangles, the length of the rib (along the side of a triangular side face), and the actual height (from the tip of the pyramid straight down to the base ).