To find the surface area of the rectangular pyramid, we need to calculate the area of each face and then sum them up.
1. The base of the pyramid is a rectangle with a length of 8mm and a width of 10mm. The area of the base is 8mm x 10mm = 80mm^2.
2. There are four triangular faces on a rectangular pyramid. The area of each triangular face can be calculated using the formula: 0.5 x base x height.
a. The first triangular face has a base of 8mm and a height of 12mm (perpendicular height to the base length). So, the area of this face is 0.5 x 8mm x 12mm = 48mm^2.
b. The second triangular face has a base of 10mm and a height of 12mm. So, the area of this face is 0.5 x 10mm x 12mm = 60mm^2.
c. The third triangular face has a base of 8mm and a height of 15mm (perpendicular height to the base width). So, the area of this face is 0.5 x 8mm x 15mm = 60mm^2.
d. The fourth triangular face has a base of 10mm and a height of 15mm. So, the area of this face is 0.5 x 10mm x 15mm = 75mm^2.
3. Now, sum up the areas of all the faces:
80mm^2 (base) + 48mm^2 + 60mm^2 + 60mm^2 + 75mm^2 = 323mm^2
Therefore, the surface area of the rectangular pyramid is 323 mm^2.
use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is 8 millimeters and the width 10 millimeters. The perpendicular heights from the apex to the base length is 12 millimeters and to the base width is 15 millimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
what is the surface area of the rectangular pyramid?
__ mm^2
3 answers
not right
I apologize for the mistake. Let's calculate the surface area of the rectangular pyramid correctly.
To calculate the surface area of a rectangular pyramid, we need to find the area of the base and the area of each triangular face. Then, we sum these areas.
1. The area of the base (rectangle):
Area_base = length x width = 8mm x 10mm = 80mm^2
2. The area of each triangular face (using the formula 1/2 * base * height):
a. Triangular face with base 8mm and height 12mm:
Area_triangular1 = 1/2 * 8mm * 12mm = 48mm^2
b. Triangular face with base 10mm and height 12mm:
Area_triangular2 = 1/2 * 10mm * 12mm = 60mm^2
c. Triangular face with base 8mm and height 15mm:
Area_triangular3 = 1/2 * 8mm * 15mm = 60mm^2
d. Triangular face with base 10mm and height 15mm:
Area_triangular4 = 1/2 * 10mm * 15mm = 75mm^2
3. Sum up the areas of the base and the triangular faces:
Surface area = Area_base + Area_triangular1 + Area_triangular2 + Area_triangular3 + Area_triangular4
Surface area = 80mm^2 + 48mm^2 + 60mm^2 + 60mm^2 + 75mm^2
Surface area = 323mm^2
Therefore, the correct surface area of the rectangular pyramid is 323 mm^2.
To calculate the surface area of a rectangular pyramid, we need to find the area of the base and the area of each triangular face. Then, we sum these areas.
1. The area of the base (rectangle):
Area_base = length x width = 8mm x 10mm = 80mm^2
2. The area of each triangular face (using the formula 1/2 * base * height):
a. Triangular face with base 8mm and height 12mm:
Area_triangular1 = 1/2 * 8mm * 12mm = 48mm^2
b. Triangular face with base 10mm and height 12mm:
Area_triangular2 = 1/2 * 10mm * 12mm = 60mm^2
c. Triangular face with base 8mm and height 15mm:
Area_triangular3 = 1/2 * 8mm * 15mm = 60mm^2
d. Triangular face with base 10mm and height 15mm:
Area_triangular4 = 1/2 * 10mm * 15mm = 75mm^2
3. Sum up the areas of the base and the triangular faces:
Surface area = Area_base + Area_triangular1 + Area_triangular2 + Area_triangular3 + Area_triangular4
Surface area = 80mm^2 + 48mm^2 + 60mm^2 + 60mm^2 + 75mm^2
Surface area = 323mm^2
Therefore, the correct surface area of the rectangular pyramid is 323 mm^2.
2 answers