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Drow the net and find CSA & Volume

Mathematics

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2 parts
b

8.1 m28.1 \text{ m}^2

c

0.75 m30.75 \text{ m}^3

Step-by-step solution

6 steps

The image shows a triangular prism with the following dimensions:

  • Base of the triangular face: 1.2 m1.2 \text{ m}
  • Height of the triangular face: 0.5 m0.5 \text{ m}
  • Hypotenuse of the triangular face: 1.3 m1.3 \text{ m}
  • Length of the prism: 2.5 m2.5 \text{ m}

Part a

**Draw the net

The net of this triangular prism consists of two identical right-angled triangles (the bases) and three rectangular faces.
Imagine unfolding the prism:

  • Two triangles, each with sides 0.5 m0.5 \text{ m}, 1.2 m1.2 \text{ m}, and 1.3 m1.3 \text{ m}.
  • Three rectangles:
    • One rectangle with dimensions 1.2 m×2.5 m1.2 \text{ m} \times 2.5 \text{ m} (corresponding to the base of the triangle).
    • One rectangle with dimensions 0.5 m×2.5 m0.5 \text{ m} \times 2.5 \text{ m} (corresponding to the height of the triangle).
    • One rectangle with dimensions 1.3 m×2.5 m1.3 \text{ m} \times 2.5 \text{ m} (corresponding to the hypotenuse of the triangle). These three rectangles would be connected side-by-side, forming a larger rectangle with dimensions (1.2+0.5+1.3) m×2.5 m(1.2 + 0.5 + 1.3) \text{ m} \times 2.5 \text{ m}, and the two triangles would be attached to opposite sides of one of the rectangles (e.g., the 1.2 m×2.5 m1.2 \text{ m} \times 2.5 \text{ m} rectangle).

Part b

8.1 m28.1 \text{ m}^2

**Find the Total Surface Area (TSA)

  1. Calculate the area of one triangular base (AbA_b).

    Ab=12×base×heightA_b = \frac{1}{2} \times \text{base} \times \text{height} Ab=12×1.2 m×0.5 m=0.3 m2A_b = \frac{1}{2} \times 1.2 \text{ m} \times 0.5 \text{ m} = 0.3 \text{ m}^2
  2. Calculate the perimeter of the triangular base (PbP_b).

    Pb=1.2 m+0.5 m+1.3 m=3.0 mP_b = 1.2 \text{ m} + 0.5 \text{ m} + 1.3 \text{ m} = 3.0 \text{ m}
  3. Calculate the lateral surface area (AlateralA_{\text{lateral}}).

    Alateral=Pb×length of prismA_{\text{lateral}} = P_b \times \text{length of prism} Alateral=3.0 m×2.5 m=7.5 m2A_{\text{lateral}} = 3.0 \text{ m} \times 2.5 \text{ m} = 7.5 \text{ m}^2
  4. Calculate the Total Surface Area (TSA).

    TSA=2×Ab+AlateralTSA = 2 \times A_b + A_{\text{lateral}} TSA=2×0.3 m2+7.5 m2=0.6 m2+7.5 m2=8.1 m2TSA = 2 \times 0.3 \text{ m}^2 + 7.5 \text{ m}^2 = 0.6 \text{ m}^2 + 7.5 \text{ m}^2 = 8.1 \text{ m}^2

    The Total Surface Area is 8.1 m2\boxed{8.1 \text{ m}^2}.

Part c

0.75 m30.75 \text{ m}^3

**Find the Volume

  1. Calculate the area of the triangular base (AbA_b).

    (This is the same as calculated in Step 1 for TSA)

    Ab=12×1.2 m×0.5 m=0.3 m2A_b = \frac{1}{2} \times 1.2 \text{ m} \times 0.5 \text{ m} = 0.3 \text{ m}^2
  2. Calculate the volume (VV) of the prism.

    V=Ab×length of prismV = A_b \times \text{length of prism} V=0.3 m2×2.5 m=0.75 m3V = 0.3 \text{ m}^2 \times 2.5 \text{ m} = 0.75 \text{ m}^3

    The Volume is 0.75 m3\boxed{0.75 \text{ m}^3}.

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