Find the surface area of a rectangular pyramid with these measurements length equals 15 m with equals 12 m and height equals 10 m
To find the surface area of a rectangular pyramid, you need to find the area of each face and then add them together.
First, let's calculate the area of the base:
The base of a rectangular pyramid is a rectangle, so the area of the base is length times width:
Area of base = length × width = 15 m × 12 m = 180 m².
Next, let's calculate the areas of the four triangular faces:
Each triangular face of the pyramid is a right-angled triangle, and the formula for the area of a triangle is 1/2 × base × height.
The base of each triangular face is the length or the width of the base rectangle (since they are all congruent), which is 15 m.
The height of each triangular face is the slant height of the pyramid, which can be found using the Pythagorean theorem:
Slant height = √(height² + (1/2 × width)²) = √(10 m² + (1/2 × 12 m)²) = √(100 m² + 36 m²) = √(136 m²) = 2√34 m.
Now, we can find the area of each triangular face using the base and the height:
Area of each triangular face = 1/2 × base × height = 1/2 × 15 m × 2√34 m = 15√34 m².
Lastly, we add up the areas of the base and the four triangular faces to find the total surface area:
Total surface area = area of base + 4 × area of each triangular face
Total surface area = 180 m² + 4 × 15√34 m²
Total surface area = 180 m² + 60√34 m².
Therefore, the surface area of the rectangular pyramid is 180 m² + 60√34 m².