Answer:
Step-by-step explanation:
[tex]V_p = b \cdot h \cdot w[/tex], where b, h, w are base, height and width respectively.
[tex]V_{sp} = \frac{1}{3} \cdot {A_b} \cdot h[/tex], where h is the height, and A_b is the area of the base.
First let's calculate the volume of the paralelipiped by the first formula.
[tex]V_p = 7 \cdot 4 \cdot 3 = 84 in^2[/tex]
Then let's find out the height of the pyramid, which is 12 - 4 = 8 in.(See drawing)
Then the area of the base of the square pyramid is simply.
[tex]A_r = 3 \cdot 7 = 21 in^2[/tex]
Now we can find the volume of the pyramid.
[tex]V_{sp} = \frac{1}{3} \cdot 21 \cdot 8 = 56 in^3[/tex]
To find the total volume, let's add both volumes.
[tex]V_T = 84 + 56 = 140 in^3[/tex]
