Question

Find the surface area of the pyramid. A triangular pyramid. The base triangle has a base of 8 meters and a height of 6.9 meters. The height of a triangular face is labeled 7 meters. The surface area is square meters.

Answer 1

To find the area of a triangle in square meters from millimeters, convert the base and height to meters, apply the area formula, and express the answer in three significant figures due to the precision of the given measurements.

Step-by-step explanation:

To find the area of a triangle in square meters when given the base in millimeters (mm) and height in millimeters (mm), we use the formula Area = 1/2 × base × height. First, it's important to convert the dimensions to meters by dividing them by 1000, since 1000mm = 1m. Once we have the correct units, we can apply the formula.

For example:

1. Convert the base from mm to meters: 166 mm / 1000 = 0.166 meters.
2. Convert the height from mm to meters: 930.0 mm / 1000 = 0.930 meters.
3. Calculate the area using the converted measurements: Area = 1/2 × 0.166 m × 0.930 m.
4. Perform the multiplication: Area = 1/2 × 0.15438 m².
5. Compute the final area: Area = 0.07719 m².

When expressing the answer, we must consider significant figures. The base was given to three significant figures and the height to four, so we should round our answer to three significant figures: Area = 0.0772 m².