Question

1. 100° 120° 100° 46. b = 147 cm² volume = 1323 cm³

Explanation:

1. For problem 46 (finding the height of a prism):

• Explanation:
• Step 1: Recall the volume - formula for a prism

The volume formula for a prism is \(V = Bh\), where \(V\) is the volume, \(B\) is the base - area, and \(h\) is the height.

• Step 2: Solve for the height \(h\)

We can re - arrange the formula \(V = Bh\) to \(h=\frac{V}{B}\). Given that \(V = 1323\mathrm{cm}^3\) and \(B = 147\mathrm{cm}^2\), then \(h=\frac{1323}{147}\).
Calculate \(\frac{1323}{147}=9\mathrm{cm}\).

• Answer: \(9\mathrm{cm}\)

Since the first problem (finding \(x\) in a polygon) is not fully described (no question about what \(x\) represents in terms of angles or side - lengths), we focus on the second problem (finding the height of a prism). The problem of finding the height of a prism is a geometry problem in the Mathematics discipline. The step - by - step format is used as it involves calculations based on a geometric formula.

Answer:

1. For problem 46 (finding the height of a prism):

• Explanation:
• Step 1: Recall the volume - formula for a prism

The volume formula for a prism is \(V = Bh\), where \(V\) is the volume, \(B\) is the base - area, and \(h\) is the height.

• Step 2: Solve for the height \(h\)

We can re - arrange the formula \(V = Bh\) to \(h=\frac{V}{B}\). Given that \(V = 1323\mathrm{cm}^3\) and \(B = 147\mathrm{cm}^2\), then \(h=\frac{1323}{147}\).
Calculate \(\frac{1323}{147}=9\mathrm{cm}\).

• Answer: \(9\mathrm{cm}\)

Since the first problem (finding \(x\) in a polygon) is not fully described (no question about what \(x\) represents in terms of angles or side - lengths), we focus on the second problem (finding the height of a prism). The problem of finding the height of a prism is a geometry problem in the Mathematics discipline. The step - by - step format is used as it involves calculations based on a geometric formula.