Answer:
The volume of the solid is either 346.5 in³ or 693 in³.
Step-by-step explanation:
The solid can either be a triangular prism or a rectangular cube.
- Consider the solid as a triangular prism.
The volume of a triangular prism is:
![V=(\frac{B\times H}{2})\times L](https://tex.z-dn.net/?f=V%3D%28%5Cfrac%7BB%5Ctimes%20H%7D%7B2%7D%29%5Ctimes%20L)
Here,
B = base
H = height
L = length
Let,
B = 7 in
H = 9 in
L = 11 in
Compute the volume of a triangular prism as follows:
![V=(\frac{B\times H}{2})\times L](https://tex.z-dn.net/?f=V%3D%28%5Cfrac%7BB%5Ctimes%20H%7D%7B2%7D%29%5Ctimes%20L)
![=(\frac{7\times 9}{2})\times11\\\\=346.5\ \text{in}^{3}](https://tex.z-dn.net/?f=%3D%28%5Cfrac%7B7%5Ctimes%209%7D%7B2%7D%29%5Ctimes11%5C%5C%5C%5C%3D346.5%5C%20%5Ctext%7Bin%7D%5E%7B3%7D)
Thus, the volume of a triangular prism is 346.5 in³.
- Consider the solid as a rectangular cube.
The volume of a rectangular cube is:
![V=L\times B\times H](https://tex.z-dn.net/?f=V%3DL%5Ctimes%20B%5Ctimes%20H)
The values of L, B and H remains the same as above.
Compute the volume of a rectangular cube as follows:
![V=L\times B\times H](https://tex.z-dn.net/?f=V%3DL%5Ctimes%20B%5Ctimes%20H)
![=11\times 7\times 9\\=693\ \text{in}^{3}](https://tex.z-dn.net/?f=%3D11%5Ctimes%207%5Ctimes%209%5C%5C%3D693%5C%20%5Ctext%7Bin%7D%5E%7B3%7D)
Thus, the volume of a rectangular cube is 693 in³.
Answer:
The answer to your question is Apothem = 9 cm
Step-by-step explanation:
Data
Area = 216 cm²
Perimeter = 48 cm
Formula
Area = Perimeter x apothem / 2
Perimeter = length of the side x number of sides
Process
Substitute the values in the area formula and simplify it.
1.- Substitution
216 = 48a/2
-Solve for a
216 x 2 = 48a
432 = 48a
a = 432 / 48
-Result
a = 9 cm
A(b+c)=ab+ac
distributive property