To solve for the area of the triangular base, height of the triangular prism, and its volume, let's start with the information given:
Step 1: Area of the Triangular Base
We need to identify the dimensions of the triangular base. If we assume the side lengths of the triangle are 5 cm, 3 cm, and 4 cm, we can use Heron's formula to find the area of the triangle.
Calculate the semi-perimeter (s): \[ s = \frac{a + b + c}{2} = \frac{5 + 3 + 4}{2} = \frac{12}{2} = 6 \text{ cm} \]
Using Heron’s Formula for the area (A): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] \[ A = \sqrt{6(6-5)(6-3)(6-4)} = \sqrt{6 \cdot 1 \cdot 3 \cdot 2} = \sqrt{36} = 6 \text{ square centimeters} \]
Step 2: Height of the Triangular Prism
The height of the prism is given as 11 cm.
Step 3: Volume of the Triangular Prism
The volume (V) of the prism can be calculated using the formula: \[ V = \text{Base Area} \times \text{Height} \] \[ V = 6 \text{ cm}^2 \times 11 \text{ cm} = 66 \text{ cubic centimeters} \]
Summary of Results
- Area of the triangular base: 6 square centimeters
- Height of the triangular prism: 11 centimeters
- Volume of the triangular prism: 66 cubic centimeters