Find a surface area of the rectangular pyramid with the measurement length equals 8 cm, equals 4 cm and equals 2 cm express your answer as a decimal round to the nearest 101 points
To find the surface area of a rectangular pyramid, we need to calculate the area of each of its faces and add them together.
The rectangular pyramid has one rectangular base and four triangular faces.
The area of the rectangular base is length x width. In this case, it is 8 cm x 4 cm = 32 cm².
The area of each triangular face can be calculated as (1/2) x base x height. The base of each triangle is the length of the rectangular base, which is 8 cm. The height of each triangle is the slant height of the pyramid, which can be calculated using the Pythagorean theorem.
The slant height can be calculated as the square root of [(length/2)² + height²]. In this case, it is the square root of [(8/2)² + 2²] = square root of (16 + 4) = square root of 20 = 2√5 cm.
Now we can calculate the area of each of the triangular faces:
Area1 = (1/2) x 8 cm x 2√5 cm = 8√5 cm²
Area2 = (1/2) x 4 cm x 2√5 cm = 4√5 cm²
Area3 = (1/2) x 8 cm x 2√5 cm = 8√5 cm²
Area4 = (1/2) x 4 cm x 2√5 cm = 4√5 cm²
Adding up all the areas, we get:
Total surface area = 32 cm² + 8√5 cm² + 4√5 cm² + 8√5 cm² + 4√5 cm²
To express the answer as a decimal rounded to the nearest hundredth, we can calculate the approximate value of √5:
√5 ≈ 2.24
Plugging in this value, we have:
Total surface area ≈ 32 cm² + 8 * 2.24 cm² + 4 * 2.24 cm² + 8 * 2.24 cm² + 4 * 2.24 cm²
Simplifying the expression, we get:
Total surface area ≈ 32 cm² + 17.92 cm² + 8.96 cm² + 17.92 cm² + 8.96 cm²
Adding up all the terms, we get:
Total surface area ≈ 85.76 cm²
Therefore, the surface area of the rectangular pyramid is approximately 85.76 cm².