Question

What is the area of one square base of this right prism?

Answer 1

To calculate the area of a triangle in square meters, convert the base and height from millimeters to meters, apply the formula (1/2) × base × height, and report the result to the correct number of significant figures, which in this case is 0.0772 m².

Step-by-step explanation:

To calculate the area of a triangle, we use the formula (1/2) × base × height. To express the area in square meters, we need to convert the measurements from millimeters to meters. There are 1000 millimeters in a meter, so the base would be 166 mm / 1000 = 0.166 meters, and the height would be 930.0 mm / 1000 = 0.930 meters.

Now, using the formula:
Area = (1/2) × 0.166 m × 0.930 m
= 0.07719 m²

Considering significant figures, since the base has three significant figures and the height has four, our final answer should be reported with three significant figures. Thus, we round the area to 0.0772 m².

Answer 2

To find the area of a triangle with a base of 166 mm and height of 930.0 mm, convert to meters and then use the triangle area formula to get 0.0772 m², given the significant figures.

Step-by-step explanation:

To calculate the area of a triangle given the base and the height, you can use the formula Area = 1/2 × base × height. For a triangle with a base of 166 mm and a height of 930.0 mm, first you need to convert millimeters to meters since the question asks for the area in square meters.

You do this by dividing each dimension by 1000: Base = 166 mm / 1000 = 0.166 m, Height = 930.0 mm / 1000 = 0.930 m. Then, apply the formula: Area = 1/2 × 0.166 m × 0.930 m.

The calculated area is 0.07719 m², which we express as 0.077 m² to maintain the proper number of significant figures, given the precision of the measurements provided.