Question
Use the image to answer the question. What is the surface area of the rectangular pyramid? (1 point) cm2 Skip to navigation
10cm 10.6cm 14cm 12cm
10cm 10.6cm 14cm 12cm
Answers
GPT 3.5
To find the surface area of a rectangular pyramid, we need to calculate the area of each of the five faces and then add them together.
The formula for the surface area of a rectangular pyramid is:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
In this case, the base of the rectangular pyramid is a rectangle with dimensions 10 cm by 14 cm. The area of the base is:
Base Area = 10 cm * 14 cm = 140 cm^2
The slant height of the pyramid is the height of one of the triangle faces. We can find the slant height by using the Pythagorean theorem:
Slant Height = sqrt(10.6^2 + 12^2) = sqrt(112.36 + 144) = sqrt(256.36) = 16.01 cm
Now, we can calculate the surface area:
Surface Area = 140 cm^2 + (1/2) * (10 cm + 14 cm) * 16.01 cm = 140 cm^2 + 24.01 cm * 16.01 cm = 140 cm^2 + 384.2421 cm^2 = 524.2421 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 524.24 cm^2.
The formula for the surface area of a rectangular pyramid is:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
In this case, the base of the rectangular pyramid is a rectangle with dimensions 10 cm by 14 cm. The area of the base is:
Base Area = 10 cm * 14 cm = 140 cm^2
The slant height of the pyramid is the height of one of the triangle faces. We can find the slant height by using the Pythagorean theorem:
Slant Height = sqrt(10.6^2 + 12^2) = sqrt(112.36 + 144) = sqrt(256.36) = 16.01 cm
Now, we can calculate the surface area:
Surface Area = 140 cm^2 + (1/2) * (10 cm + 14 cm) * 16.01 cm = 140 cm^2 + 24.01 cm * 16.01 cm = 140 cm^2 + 384.2421 cm^2 = 524.2421 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 524.24 cm^2.