Answer:
[tex]\huge\boxed{49.9\text{ cm}^3}[/tex]
Step-by-step explanation:
The general form for the volume of a prism is:
[tex]V=A_b \cdot h[/tex]
where:
- [tex]A_b[/tex] = area of base
- [tex]h[/tex] = height
We can identify the base as a triangle, which means its area formula is:
[tex]A_\triangle = \dfrac{1}{2}bh_\triangle[/tex]
where:
- [tex]b[/tex] = length of base
- [tex]h_\triangle[/tex] = height of triangle base (NOT height of the prism)
Plugging in the given values, we get:
[tex]A_b = \dfrac{1}2 (8.7\text{ cm}) (2.67\text{ cm})[/tex]
[tex]A_b = 11.6145\text{ cm}^2[/tex]
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Notice, for calculating the area of the triangle, how we use the base length for which we have a height that is perpendicular to that base.
We couldn't have used 8.3 cm as the base because we aren't given a height value perpendicular to it.
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Now, using this triangle base area, we can solve for the prism's volume:
[tex]V=A_b \cdot h[/tex]
[tex]V = (11.6145\text{ cm}^2)(4.3\text{ cm})[/tex]
[tex]\boxed{V \approx 49.9\text{ cm}^3}[/tex]
