\( H \)
\( h_\mathrm{s} \)
\( h_\mathrm{b} \)
\( a \)
\( h_\mathrm{b} \) \( = \sqrt{\color{#00BFFF}{a}^2 - {(\frac{\color{#00BFFF}{a}}{2})}^2} \)
Surface area \( \space = \space \)
Area of base \( + \space 3 \space × \) Area of each triangular face
\( = \space \Bigr( \frac{1}{2} \space \) \( a \) \( × \) \( h_\mathrm{b} \) \(\Bigr{)} + \space 3 \space × \Bigr( \frac{1}{2} \) \( a \) \( × \) \( h_\mathrm{s} \) \( \Bigr) \)
\( = \space \Bigr( \frac{1}{2} \space ×\) \(10\) \( × \) \( 34{,}64 \) \( \Bigr{)} + \space 3 \space × \Bigr( \frac{1}{2} \space × \) \(10\) \( × \)\(60\)\( \Bigr) \)
\( = \space 4\space292{,}8\) square units
Volume
\( \space = \frac{1}{3} \space × \) Area of base \( × \) height of pyramid
\( = \frac{1}{3} \space ×\frac{1}{2} \space \) \( a \) \( × \) \( h_\mathrm{b} \) \( × \) \( H \)
\( = \frac{1}{3}\space ×\frac{1}{2} \space × \) \( 10 \) \( × \) \( 34{,}64 \) \( × \) \( 58{,}88 \)
\( = 13\space597{,}35\) cubic units
2
2
2
2
Surface area
\( = \space \) Area of base\( \space + \space 4 \space × \) Area of each triangular face
\(= \space \) \( a \) \( \space + \space 4 \space × \space \Bigr( \frac{1}{2} \) \( \tiny{a} \) \( × \) \( h_\mathrm{s} \)\( \Bigr) \)
\(= \space ( \)\( 10 \)\( ) \space + \space 4 \space × \space \Bigr( \frac{1}{2} \space × \) \( 10 \)\(\space × \) \( 60 \) \( \Bigr) \) \(= \space 1 \space600 + 4 \space × \space 1\space200 \) \(= \space 6\space400\) square units
\(= \space \) \( a \) \( \space + \space 4 \space × \space \Bigr( \frac{1}{2} \) \( \tiny{a} \) \( × \) \( h_\mathrm{s} \)\( \Bigr) \)
\(= \space ( \)\( 10 \)\( ) \space + \space 4 \space × \space \Bigr( \frac{1}{2} \space × \) \( 10 \)\(\space × \) \( 60 \) \( \Bigr) \) \(= \space 1 \space600 + 4 \space × \space 1\space200 \) \(= \space 6\space400\) square units
Volume
\( = \frac{1}{3} \space × \) Area of base \( × \) height of pyramid
\( = \frac{1}{3} \space × \) \( a \space \)\( \space × \) \( H \)
\( = \frac{1}{3} \space × ( \)\(10\)\( ) \space \space × \) \( 56{,}57 \)
\( = 30\space170{,}67\) cubic units
11
10
10
- This simulation shows you how the surface area and volume of a right pyramid change when the side of its base and its slant height are changed.
- Use the sliders to set the side of the base and the slant height of the right pyramid.
- The height of the pyramid (the vertical height) varies automatically when the side of the base and slant height are varied.
- You can also vary the height of the pyramid instead of its slant height.
- Look carefully at all the values that appear on the screen.
- Click RESET to start again.
