Find Surface Area Using Nets - 6th Grade Math
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State the area formula for a rectangle with length $l$ and width $w$.
State the area formula for a rectangle with length $l$ and width $w$.
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$A = lw$. Rectangle area equals length times width.
$A = lw$. Rectangle area equals length times width.
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What is surface area of a $3$D figure in terms of its net?
What is surface area of a $3$D figure in terms of its net?
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Sum of the areas of all faces in the net. Surface area equals the total area of all faces when the net is laid flat.
Sum of the areas of all faces in the net. Surface area equals the total area of all faces when the net is laid flat.
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Which option describes a correct strategy to find surface area from a net?
Which option describes a correct strategy to find surface area from a net?
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Add the areas of all faces; do not count overlaps. Surface area is the sum of all face areas without double-counting.
Add the areas of all faces; do not count overlaps. Surface area is the sum of all face areas without double-counting.
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What is the surface area formula for a cube with side length $s$?
What is the surface area formula for a cube with side length $s$?
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$SA = 6s^2$. A cube has 6 identical square faces.
$SA = 6s^2$. A cube has 6 identical square faces.
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What is the surface area formula for a rectangular prism with dimensions $l$, $w$, and $h$?
What is the surface area formula for a rectangular prism with dimensions $l$, $w$, and $h$?
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$SA = 2(lw + lh + wh)$. Accounts for 3 pairs of opposite rectangular faces.
$SA = 2(lw + lh + wh)$. Accounts for 3 pairs of opposite rectangular faces.
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Identify the surface area of a cube with $s = 4$.
Identify the surface area of a cube with $s = 4$.
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$96$. Apply $SA = 6s^2 = 6(4)^2 = 6(16) = 96$.
$96$. Apply $SA = 6s^2 = 6(4)^2 = 6(16) = 96$.
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What faces appear in the net of a rectangular prism (in terms of shapes and counts)?
What faces appear in the net of a rectangular prism (in terms of shapes and counts)?
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$6$ rectangles. Has 3 pairs of opposite rectangular faces.
$6$ rectangles. Has 3 pairs of opposite rectangular faces.
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Find the missing dimension: A rectangle has area $24$ and width $w=6$; what is $l$?
Find the missing dimension: A rectangle has area $24$ and width $w=6$; what is $l$?
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$4$. Since $A = lw$, then $l = A/w = 24/6 = 4$.
$4$. Since $A = lw$, then $l = A/w = 24/6 = 4$.
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Find the missing height: A triangle has area $18$ and base $b=6$; what is $h$?
Find the missing height: A triangle has area $18$ and base $b=6$; what is $h$?
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$6$. Since $A = rac{1}{2}bh$, then $h = 2A/b = 2(18)/6 = 6$.
$6$. Since $A = rac{1}{2}bh$, then $h = 2A/b = 2(18)/6 = 6$.
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Which measurement is needed for the area of a triangular face: side length or perpendicular height?
Which measurement is needed for the area of a triangular face: side length or perpendicular height?
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Perpendicular height. Height must be perpendicular to base for area formula.
Perpendicular height. Height must be perpendicular to base for area formula.
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Find the surface area of a rectangular prism with dimensions $2$, $3$, and $4$.
Find the surface area of a rectangular prism with dimensions $2$, $3$, and $4$.
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$52$. $2(2 imes 3) + 2(2 imes 4) + 2(3 imes 4) = 52$.
$52$. $2(2 imes 3) + 2(2 imes 4) + 2(3 imes 4) = 52$.
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Find the total area of $2$ rectangles each with area $18$ and $4$ triangles each with area $6$.
Find the total area of $2$ rectangles each with area $18$ and $4$ triangles each with area $6$.
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$60$. $2(18) + 4(6) = 36 + 24 = 60$.
$60$. $2(18) + 4(6) = 36 + 24 = 60$.
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Find the surface area of a triangular prism net with $3$ rectangles of areas $12$, $15$, $9$ and $2$ triangles of area $6$ each.
Find the surface area of a triangular prism net with $3$ rectangles of areas $12$, $15$, $9$ and $2$ triangles of area $6$ each.
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$48$. $12 + 15 + 9 + 2(6) = 48$.
$48$. $12 + 15 + 9 + 2(6) = 48$.
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Find the surface area of a square pyramid net with base $6\times 6$ and $4$ triangles each with $b=6$, $h=5$.
Find the surface area of a square pyramid net with base $6\times 6$ and $4$ triangles each with $b=6$, $h=5$.
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$96$. $36 + 4( rac{1}{2} imes 6 imes 5) = 36 + 60 = 96$.
$96$. $36 + 4( rac{1}{2} imes 6 imes 5) = 36 + 60 = 96$.
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A net has faces with areas $20$, $20$, $30$, $30$, $24$, and $24$. What is the surface area?
A net has faces with areas $20$, $20$, $30$, $30$, $24$, and $24$. What is the surface area?
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$148$. Add all face areas: $20 + 20 + 30 + 30 + 24 + 24 = 148$.
$148$. Add all face areas: $20 + 20 + 30 + 30 + 24 + 24 = 148$.
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Identify the surface area if the net has $6$ congruent squares, each with side length $x$.
Identify the surface area if the net has $6$ congruent squares, each with side length $x$.
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$6x^2$. Each square has area $x^2$; total is $6x^2$.
$6x^2$. Each square has area $x^2$; total is $6x^2$.
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Find and correct the error: A student adds only the $4$ side faces of a prism net and calls it surface area.
Find and correct the error: A student adds only the $4$ side faces of a prism net and calls it surface area.
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Include all faces, including both bases, in the total. Surface area must include all 6 faces of a prism.
Include all faces, including both bases, in the total. Surface area must include all 6 faces of a prism.
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A gift box is a closed rectangular prism with dimensions $8$, $3$, and $2$. What is the wrapping paper area needed (no overlap)?
A gift box is a closed rectangular prism with dimensions $8$, $3$, and $2$. What is the wrapping paper area needed (no overlap)?
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$100$. $2(8 imes 3) + 2(8 imes 2) + 2(3 imes 2) = 100$.
$100$. $2(8 imes 3) + 2(8 imes 2) + 2(3 imes 2) = 100$.
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What is the surface area of a 3D figure in terms of its net?
What is the surface area of a 3D figure in terms of its net?
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The sum of the areas of all faces in the net. A net shows all faces unfolded; surface area adds them all.
The sum of the areas of all faces in the net. A net shows all faces unfolded; surface area adds them all.
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A cube-shaped box has surface area $216$. What is the edge length?
A cube-shaped box has surface area $216$. What is the edge length?
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$6$. $6x^2 = 216$, so $x^2 = 36$ and $x = 6$.
$6$. $6x^2 = 216$, so $x^2 = 36$ and $x = 6$.
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What is the area formula for a rectangle with length $l$ and width $w$?
What is the area formula for a rectangle with length $l$ and width $w$?
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$A = lw$. Rectangle area equals length times width.
$A = lw$. Rectangle area equals length times width.
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What is the area formula for a triangle with base $b$ and height $h$?
What is the area formula for a triangle with base $b$ and height $h$?
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$A = rac{1}{2}bh$. Triangle area is half the base times height.
$A = rac{1}{2}bh$. Triangle area is half the base times height.
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Identify the two 3D figures whose nets can be made only from rectangles.
Identify the two 3D figures whose nets can be made only from rectangles.
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Rectangular prism and cube. Both have 6 rectangular faces when unfolded.
Rectangular prism and cube. Both have 6 rectangular faces when unfolded.
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What is the surface area of a solid in terms of its net?
What is the surface area of a solid in terms of its net?
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The sum of the areas of all faces in the net. Each face contributes its area to the total surface area.
The sum of the areas of all faces in the net. Each face contributes its area to the total surface area.
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Identify the two types of faces used in nets for many prisms and pyramids in Grade $6$.
Identify the two types of faces used in nets for many prisms and pyramids in Grade $6$.
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Rectangles and triangles. These basic shapes compose the faces of common 3D figures.
Rectangles and triangles. These basic shapes compose the faces of common 3D figures.
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