The volume of any prism is the product of its base area (B) and height (h). Here, the base is a pentagon, so finding its area requires a couple of steps.
The pentagonal end area can be divided into a 5 in × 6 in rectangle, and a triangle that has a base of 5 in and a height of 8 in.
The area of the rectangle is the product of its dimensions:
... rectangle area = (5 in)×(6 in) = 30 in²
The area of the triangle is half the product of its dimensions:
... triangle area = (1/2)×(5 in)×(8 in) = 20 in²
So, the total area of the penatagonal end of the prism is
... base area = rectangle area + triangle area
... base area = (30 in²) + (20 in²) = 50 in²
Then the product of base area and "height" gives the volume. Here, the "height" is the distance between the two pentagonal ends, 12 in.
... birdhouse volume = base area × height
... birdhouse volume = (50 in²) × (12 in)
... birdhouse volume = 600 in³
