what is the slant height in a rectangular or square pyramid?
the height from the apex straight down to the base of the triangular face where it forms a right angle
an edge of a triangular face
the height of the pyramid from the apex straight down to the middle of the base of the pyramid
the distance across the triangular face
3 answers
The slant height in a rectangular or square pyramid is the height from the apex straight down to the middle of the base of the pyramid.
use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 20 centimeters and the width as 18 centimeters. The perpendicular heights from the apex to the base length of 20 is 16.6 centimeters and to the base width of 18 is 17.2 centimeters. 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 of the rectangular pyramid?
1,643.2 cm^2
1,001.6 cm^2
102,787.2 cm^2
1,178.8 cm^2
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 20 centimeters and the width as 18 centimeters. The perpendicular heights from the apex to the base length of 20 is 16.6 centimeters and to the base width of 18 is 17.2 centimeters. 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 of the rectangular pyramid?
1,643.2 cm^2
1,001.6 cm^2
102,787.2 cm^2
1,178.8 cm^2
To calculate the surface area of the rectangular pyramid, we need to find the areas of each of the faces and add them all together.
1. Area of the base:
Length x Width = 20 cm x 18 cm = 360 cm^2
2. Area of each of the rectangular faces (there are 4):
(1/2) x (Base Perpendicular Height) x Base = (1/2) x 16.6 cm x 20 cm = 166 cm^2
(1/2) x 17.2 cm x 18 cm = 154.8 cm^2
3. Area of the two triangular faces:
(1/2) x Base x Slant Height = (1/2) x 20 cm x 16.6 cm = 166 cm^2
(1/2) x 18 cm x 17.2 cm = 154.8 cm^2
Total Surface Area = 360 cm^2 + 4(166 cm^2 + 154.8 cm^2) = 360 cm^2 + 4(320.8 cm^2) = 360 cm^2 + 1283.2 cm^2 = 1643.2 cm^2
Therefore, the surface area of the rectangular pyramid is 1,643.2 cm^2.
So, the correct answer is: 1,643.2 cm^2.
1. Area of the base:
Length x Width = 20 cm x 18 cm = 360 cm^2
2. Area of each of the rectangular faces (there are 4):
(1/2) x (Base Perpendicular Height) x Base = (1/2) x 16.6 cm x 20 cm = 166 cm^2
(1/2) x 17.2 cm x 18 cm = 154.8 cm^2
3. Area of the two triangular faces:
(1/2) x Base x Slant Height = (1/2) x 20 cm x 16.6 cm = 166 cm^2
(1/2) x 18 cm x 17.2 cm = 154.8 cm^2
Total Surface Area = 360 cm^2 + 4(166 cm^2 + 154.8 cm^2) = 360 cm^2 + 4(320.8 cm^2) = 360 cm^2 + 1283.2 cm^2 = 1643.2 cm^2
Therefore, the surface area of the rectangular pyramid is 1,643.2 cm^2.
So, the correct answer is: 1,643.2 cm^2.
1 answer