Plan: To find the volume of the cabin (Vcabin), I must find the volume of the rectangular prism(Vrp) and add it to the volume of the triangular prism (Vtp).

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Presentation transcript:

Plan: To find the volume of the cabin (Vcabin), I must find the volume of the rectangular prism(Vrp) and add it to the volume of the triangular prism (Vtp). Vcabin = Vrp + Vtp To calculate the volume of the rectangular prism, simply find the area of the front face (rectangle) and multiply that area by the depth of the rectangular prism

To calculate the volume of the triangular prism, simply find the area of the front face (triangle) and multiply that area by the depth of the triangular prism You must show all your calculations and use proper math terminology and units as shown!!

1.8 0.5 90 000 0.90 m2 A = bh 2 A = 1.8 m x 0.5 m A = 0.45 m2 A = l x w A = 2.2 m x 1.8 m A = 3.96 m2 x 2.2 1.8 176 220 3.96 m2 x + V = A x d V = 0.45 x 2.0 m V = 0.9 m3 V = A x d V = 3.96 x 2.0 m V = 7.92 m3 Vcabin = 7.92 m3 + 0.9 m3 = 8.82 m3

Plan: To find the surface area of the cabin (SAcabin), I must find the area of the rectangular face(Ar) and multiply it by 4 (because there are 4 congruent rectangular faces). Then find the area of the square face (As) and (I don’t multiply this by 2 because one of the square faces doesn’t exist as it is where the two 3 –D shapes combine to form the cabin). Finally, I simply add the total areas of the rectangular faces to the total areas of the square faces to find the total surface area of the rectangular prism. I still need to find the surface area of the triangular prism (roof), so I find the surface area of the triangular face and multiply it by 2 because there are 2 of them. Next, I must find the area of the rectangular face and multiply it by 2 because there are 2 rectangular faces shown at the top of the roof. Prior knowledge: In order to find the area of the roof rectangular face I must use the Pythagorean Theorem to calculate the width.

2.2 1.8 176 220 3.96 m2 SAr = l x w = 2.2 x 1.8 = 3.96 m2 SAs = l x w = 2.0 x 1.8 = 3.6 m2 x 4 for the 4 faces = 15.84 m2 SA for rectangular prism = 15.84 + 3.6 = 19.44 m2

A = bh 2 A = 1.8 m x 0.5 m A = 0.45 m2 x2 for 2 faces = 0.90 m2 Ar = l x w = 2.0 x 1.0295 = 2.05912 m2 x 2 for 2 faces = 4.11824 m2 w is C from Pythagorean Theorem: a2 + b2 = c2 so c is equal to the square root of the sum of a2 and b2 C = 1.0295 m SA for triangular prism = 4.11824 + 3.6 = 7.71824 m2

SA for cabin = 7.71824 + 19.44 = 27.15824 m2