To analyze the 3D triangular prism described, we need to ensure clarity in understanding the dimensions provided.
The dimensions of the triangular face are as follows:
- One leg (base) = 27.9 cm
- Other leg (height) = 5.1 cm
- Hypotenuse = 28.4 cm (this should be the longest side of the triangle).
From the information provided, it seems that we are dealing with a right triangle since one angle is a right angle (90 degrees). The triangle's legs are the base and the height, while the hypotenuse connects the ends of these two legs.
Area of the Triangular Face
To find the area of the triangular face:
The area \(A\) of a right triangle is calculated as: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Substituting in the values: \[ A = \frac{1}{2} \times 27.9 , \text{cm} \times 5.1 , \text{cm} = \frac{1}{2} \times 142.29 , \text{cm}^2 = 71.145 , \text{cm}^2 \]
Volume of the Prism
The volume \(V\) of a triangular prism can be calculated using the formula: \[ V = \text{Base Area} \times \text{Length} \]
Given that the length of the prism is 30.5 cm: \[ V = 71.145 , \text{cm}^2 \times 30.5 , \text{cm} \approx 2179.9125 , \text{cm}^3 \]
Therefore, the volume of the prism is approximately 2179.91 cm³.
Summary
You now have the calculations for both the area of the triangular face and the volume of the prism:
- Area of the triangular face: 71.145 cm²
- Volume of the triangular prism: 2179.91 cm³