Triangular pyramid

Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm

Result

V =  1848.423 cm3
S =  1179.436 cm2

Solution:

$a=20 \ \text{cm} \ \\ b=35 \ \text{cm} \ \\ \ \\ a_{2}=a/2=20/2=10 \ \text{cm} \ \\ h_{1}=\sqrt{ b^2-a_{2}^2 }=\sqrt{ 35^2-10^2 } \doteq 15 \ \sqrt{ 5 } \ \text{cm} \doteq 33.541 \ \text{cm} \ \\ h=\sqrt{ h_{1}^2 - a_{2}^2 }=\sqrt{ 33.541^2 - 10^2 } \doteq 5 \ \sqrt{ 41 } \ \text{cm} \doteq 32.0156 \ \text{cm} \ \\ \ \\ S_{1}=a \cdot \ h_{1} / 2=20 \cdot \ 33.541 / 2 \doteq 150 \ \sqrt{ 5 } \ \text{cm}^2 \doteq 335.4102 \ \text{cm}^2 \ \\ S_{2}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 20^2 \doteq 100 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 173.2051 \ \text{cm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{2} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 173.2051 \cdot \ 32.0156 \doteq 1848.4228 \doteq 1848.423 \ \text{cm}^3$
$S=3 \cdot \ S_{1} + S_{2}=3 \cdot \ 335.4102 + 173.2051 \doteq 1179.4357 \doteq 1179.436 \ \text{cm}^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

Next similar math problems:

1. Pyramid
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
3. Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
4. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 4 cm.
5. Lamp cone
Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
6. Cylinder - A&V
The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
7. Center traverse
It is true that the middle traverse bisects the triangle?
8. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
9. Sines
In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?