Definitions
What is surface area?
The sum of the areas of all faces of a 3-D object.
How many faces should be shown in a complete net for a rectangular prism?
6
What is the formula for finding the surface area of a rectangular prism?
SA = 2lw + 2lh + 2wh
SA = 2(lw + lh + wh)
What shapes make up the surface area of a triangular prism?
2 triangles and 3 rectangles
What is the formula for the surface area of a cylinder?
SA = 2πr² + 2πrh?
What is the difference between area and perimeter?
When we calculate area we are calculating the measurement of the surface of the shape.
When we calculate the perimeter of a shape we are combining the measurements of the exterior of the shape.
Draw a net for a rectangular prism with dimensions 3 cm × 2 cm × 1 cm. Label all faces with their dimensions.
A net with 6 rectangles:
2 faces of 3×2
2 faces of 3×1
2 faces of 2×1
Find the surface area of a rectangular prism with a length of 4 cm, width of 3 cm, and height of 2 cm.
52 cm²
(SA = 2(4×3 + 4×2 + 3×2) = 2(12 + 8 + 6) = 2(26) = 52)
A triangular prism has triangle with a base of 4 cm and height of 3 cm. The prism is 10 cm long.
Find the area of the two triangular bases.
3 x 4 = 12 cm²
Find the surface area of a cylinder with a radius of 3 cm and a height of 5 cm.
150.72 cm²
(SA = 2×3.14×9 + 2×3.14×3×5 = 56.52 + 94.2 = 150.72)
What is the difference between radius and diameter?
Radius is the distance from the edge of a circle to its centre, whereas diameter is the whole distance across through the middle of the circle.
Draw and label a net for a cylinder with a height of 8 cm and a base radius of 3 cm.
A rectangle (8 cm by circumference of the base) and 2 circles (radius 3 cm). Circumference = 2πr = approx. 18.85 cm.
A box has a length of 6 cm, width of 5 cm, and height of 2 cm. What is its surface area?
104 cm²
(SA = 2(6×5 + 6×2 + 5×2) = 2(30 + 12 + 10) = 2(52) = 104)
A triangular prism has a triangle base of 4 cm, side lengths of 5 cm, and a height of 3 cm. The length of the prism is 8 cm. What is the total surface area?
SA = (4x3) + (8x5) + (8x5) + (8x4)
SA = 12 + 40 + 40 + 32
SA = 124cm²
What is the missing side length of the rectangle equal to on a cylinder?
What is the difference between a face, an edge, and a vertex?
Face: flat or curved surface
Edge: line segment where two faces meet
Vertex: point where three or more edges meet
Create a net for a triangular prism where the triangle has sides of 6 cm, 5 cm, and 4 cm, and the prism is 7 cm long. Label all dimensions.
A net with 2 triangles (sides: 4, 5, 6 cm) and 3 rectangles:
4 × 7
5 × 7
6 × 7
Sam is wrapping a gift shaped like a rectangular prism. The box measures 10 cm long, 7 cm wide, and 4 cm tall. How much wrapping paper will she need to cover the entire box?
276 cm²
(SA = 2(10×7 + 10×4 + 7×4) = 2(70 + 40 + 28) = 2(138) = 276)
A tent is shaped like a triangular prism. The triangular face has a base of 6 m and a height of 4 m. The length of the tent is 12 m. Each of the three sides of the triangle is 5 m, 6 m, and 7 m. What is the total surface area of the tent?
Triangle area: 6 × 4 = 24
Rectangles:
5 × 12 = 60
6 × 12 = 72
7 × 12 = 84
Total = 24 + 60 + 72 + 84 = 240 m²
A soup can has a radius of 4 cm and a height of 10 cm.
How much metal is needed to cover the entire surface of the can?
351.68 cm²
(SA = 2πr² + 2πrh = 2×3.14×16 + 2×3.14×4×10 = 100.48 + 251.2 = 351.68)
What is the difference between an equilateral, isosceles, and scalene triangle?
equilateral - has three sides of equal length
isosceles - has at least two sides of equal length
scalene - has no sides of equal length
You’re drawing a net for a triangular prism with triangle sides of 5 cm, 4 cm, and 3 cm, and a prism height (length) of 10 cm. What are the dimensions of all the rectangles in the net?
3 rectangles: 5 cm × 10 cm, 4 cm × 10 cm, and 3 cm × 10 cm
A storage container is shaped like a rectangular prism. It is 12 cm long, 8 cm wide, and 5 cm tall. The lid and base will be painted one color, and the sides a different color. How much area will be painted for the sides only?
SA = 2(12×5 + 8×5) = 200 cm².
A triangular prism has a triangle base with a base of 9 cm and height of 5 cm. The other two sides of the triangle are 6 cm and 7 cm. The prism is 10 cm long.
Find the total surface area.
Triangle area: 9 × 5 = 45
Rectangles:
9 × 10 = 90
6 × 10 = 60
7 × 10 = 70
Total SA = 45 + 90 + 60 + 70 = 265 cm²
A cylindrical drum is being painted. It has a radius of 7 cm and a height of 12 cm. Only the curved surface is being painted (not the top and bottom). How much area will be painted?
527.52 cm²
(Only lateral surface: 2πrh = 2 × 3.14 × 7 × 12 = 527.52)