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Surface area of prisms and pyramids
Using nets to find the total surface area of cubes, rectangular prisms, triangular prisms and square-based pyramids.
Prisms
A triangular prism has a right-angled triangle end with sides $3$, $4$, $5$ cm and length $10$ cm. Find its surface area.
Pyramids
A square pyramid has a square base and four identical triangles. Each triangle's height is the slant height, not the vertical height.
A square pyramid has base $6$ cm and slant height $5$ cm. Find its surface area.
Triangular prism, ends $3, 4, 5$ right triangle, length $10$. Surface area?
$12 + 120$.
Square pyramid, base $6$, slant height $5$. Surface area?
$36 + 60$.
Surface area of a cube with side $4$?
$6 \times 16$.
Surface area of a $5 \times 3 \times 2$ rectangular prism?
$2(15 + 10 + 6)$.
A cube has surface area $150$ cm². Side length?
$s^2 = 25$.
An open box (no top) is $4 \times 3 \times 2$. Outside surface area?
A closed box is $2(12 + 8 + 6) = 52$; remove the $4 \times 3$ top: $52 - 12 = 40$.
Square pyramid, base $10$, slant height $13$. Surface area?
$100 + 4 \times 65$.
For a pyramid's triangular faces you need the:
The height of each triangle face.
New numbers every time. Keep going until you get five in a row.