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?
(1 point)
mm2
To find the surface area of the rectangular pyramid, we need to find the area of each of the five faces (including the base).
1. The base of the pyramid is a rectangle with length 8 mm and width 10 mm. So, the area of the base is 8 mm * 10 mm = 80 mm^2.
2. The three triangular faces have a base equal to one side of the rectangle and a height equal to the perpendicular height from the apex to that base. The area of each triangular face can be calculated as: (1/2) * base * height.
- For the face with base length 8 mm and height 12 mm: (1/2) * 8 mm * 12 mm = 48 mm^2.
- For the face with base width 10 mm and height 12 mm: (1/2) * 10 mm * 12 mm = 60 mm^2.
- For the face with base length 8 mm and height 15 mm: (1/2) * 8 mm * 15 mm = 60 mm^2.
3. The remaining two lateral faces are rectangles with sides equal to the base length and the perpendicular height. So, the area of each lateral face is 8 mm * 12 mm = 96 mm^2.
Adding up all the areas:
80 mm^2 (base) + 48 mm^2 + 60 mm^2 + 60 mm^2 + 96 mm^2 = 344 mm^2.
Therefore, the surface area of the rectangular pyramid is 344 mm^2.
wrong
My apologies for the mistake. Let's correct that.
To find the surface area of the rectangular pyramid, we need to find the areas of all the faces and add them up.
1. The base of the pyramid is a rectangle with a length of 8 mm and width of 10 mm. The area of the base is 8 mm * 10 mm = 80 mm^2.
2. The three lateral faces of the pyramid are triangles. Two of these triangles have base 8 mm and height 12 mm, and the other has base 10 mm and height 15 mm.
The formula to find the area of a triangle is (1/2) * base * height.
- Area of first lateral face: (1/2) * 8 mm * 12 mm = 48 mm^2.
- Area of second lateral face: (1/2) * 8 mm * 12 mm = 48 mm^2.
- Area of third lateral face: (1/2) * 10 mm * 15 mm = 75 mm^2.
3. To find the area of the fourth face (the other lateral face), it is a parallelogram with base 8 mm and height 15 mm. The area of a parallelogram is base * height.
- Area of the fourth lateral face: 8 mm * 15 mm = 120 mm^2.
Now, add up the areas of all the faces:
80 mm^2 (base) + 48 mm^2 + 48 mm^2 + 75 mm^2 + 120 mm^2 = 371 mm^2.
Therefore, the correct surface area of the rectangular pyramid is 371 mm^2.
the answer was 326
I apologize for the error in my previous responses. Thank you for providing the correct answer.
The surface area of the rectangular pyramid, calculated correctly, is indeed 326 mm^2. Thank you for pointing out the mistake.