Find the Surface Area
Total SA = Base Area + Lateral Area
Base = side², Lateral = 2 × side × slant height
Pyramid Surface Area!
Square Base. Choose your challenge:
Surface Area of Pyramid Game
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This Surface Area of Pyramid Game is a great way to put your skills to the test in a fun environment. By practicing, you’ll start to work out the answers efficiently.
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Surface Area of Square-based Pyramid Game
The total surface area (SA) is the sum of these two parts:
SA = Area of Base + Lateral Area
SA = s2 + 2sl
Scroll down the page for a more detailed explanation.
In this game, you may select “Find Surface Area”, “Find Lateral Area”, “Find Slant Height” or “Mixed Questions”. If you give a wrong answer, the game will provide the correct answer.
Score: 0 / 0
How to Play the Surface Area of Pyramid Game
In the game, you need to find the surface area of a pyramid or find lateral area or slant height when given the surface area.
Here’s how to play:
- Choose your challenge: Select “Find Surface Area”, “Find Lateral Area”, “Find Slant Height” or “Mixed Questions”.
- Find Surface Area: Calculate surface area given the radius.
- Find Radius: Calculate radius given the surface area.
- Enter Your Answer: Enter in the answer.
- Check Your Work: Click the “Check” button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
- Get a New Problem: Click the “Next” button for a new problem.
Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried. - Back to Menu Click “Menu” to restart the game.
The Total Surface Area Formula
The total surface area (SA) is the sum of these two parts:
SA = Area of Base + Lateral Area
1. Area of the Square Base (B)
Since the base is a square:
Area of Base = s2
2. Lateral Area (LA)
The four side faces are identical triangles.
The area of one triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\).
The base of the triangle is the side length (s).
The height of the triangle is the slant height (l).
\(\text{Area of one triangle} = \frac{1}{2} s l\).
Since there are four identical triangles:
\(\text{Lateral Area} = 4 \times \left( \frac{1}{2} s l \right) = 2 s l\)
3. The Complete Formula
Adding the two components gives the total surface area:
SA = s2 + 2sl
Where:
A is the Total Surface Area.
s is the side length of the square base.
l is the slant height of the pyramid (the height of the triangular face).
The video gives a clear, step-by-step approach to find the surface area of a pyramid.
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