To find the volume of the prism, we first need to calculate the area of the base, which consists of a rectangle and a triangle.
Step 1: Find the area of the rectangle.
The formula for the area of a rectangle is:
\[ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} \]
Given the dimensions of the rectangle:
- Length = 10 cm
- Width = 4 cm
Calculating the area:
\[ \text{Area}_{\text{rectangle}} = 10 , \text{cm} \times 4 , \text{cm} = 40 , \text{cm}^2 \]
Step 2: Find the area of the triangle.
The formula for the area of a triangle is:
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the triangle:
- Base = 10 cm (along the side of the rectangle)
- Height = 6 cm
Calculating the area:
\[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 , \text{cm} \times 6 , \text{cm} = \frac{1}{2} \times 60 = 30 , \text{cm}^2 \]
Step 3: Find the total area of the base.
The total area of the base \( B \) is the sum of the area of the rectangle and the area of the triangle:
\[ B = \text{Area}{\text{rectangle}} + \text{Area}{\text{triangle}} = 40 , \text{cm}^2 + 30 , \text{cm}^2 = 70 , \text{cm}^2 \]
Step 4: Find the height of the prism.
The height of the prism \( h \) is given as 5 cm.
Step 5: Calculate the volume of the prism.
The volume \( V \) of the prism is calculated using the formula:
\[ V = B \times h \]
Substituting the values we found:
\[ V = 70 , \text{cm}^2 \times 5 , \text{cm} = 350 , \text{cm}^3 \]
Summary:
- Area of the base, \( B = 70 , \text{cm}^2 \)
- Height of the prism, \( h = 5 , \text{cm} \)
- Volume, \( V = 350 , \text{cm}^3 \)
The final answer to enter is:
- Volume = 350 cm³.