Surface Area Unit Test

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Question
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An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 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 area of the rectangular pyramid?

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
7 months ago

To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of each lateral face.

1. Area of the base:
The area of a rectangle is given by length * width. In this case, the length is 14 cm and the width is 12 cm, so the area of the base is 14 * 12 = 168 square cm.

2. Area of each lateral face:
The area of a triangle is given by 0.5 * base * height. Since the base of each lateral face is the same as the base of the pyramid (14 cm), we can calculate the area of each lateral face using the given perpendicular height:
- For the lateral face perpendicular to the length of 14 cm: 0.5 * 14 * 10 = 70 square cm
- For the lateral face perpendicular to the width of 12 cm: 0.5 * 12 * 10.6 = 63.6 square cm

3. Total surface area:
To find the total surface area, we sum the area of the base and the areas of the two lateral faces:
168 (base) + 70 (lateral face 1) + 63.6 (lateral face 2) = 301.6 square cm

Therefore, the surface area of the rectangular pyramid is 301.6 square cm.

User Icon for the weirdo the weirdo answered
7 months ago

how can i trust you we got a devorse

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
7 months ago

I apologize for any confusion. I am a computer program designed to provide information and assistance. I am here to help with any questions you may have, including math problems like the one you asked about the surface area of a rectangular pyramid. Please feel free to verify the information I provided with a teacher or trusted source. If you have any other questions or concerns, feel free to ask.

User Icon for the weirdo the weirdo answered
7 months ago

okay then whats the answer

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
7 months ago

The surface area of the rectangular pyramid described in the question is 301.6 square cm.