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Here are a few recommended readings before getting started with this lesson.
Paulina enjoys creating origami objects. After she made the three congruent origami pyramids shown below, she noticed that they could form a cube.
When the base area and the height of a pyramid are known, its volume can be calculated.
Architects might enjoy turning things upside down. Maya is interested in architecture and follows some online magazines about it. After reading an article about the Slovak Radio Building in Bratislava, Slovakia, she wonders about the area of the square rooftop.
If the height of the building is 80 meters and its volume is about 245760 cubic meters, find the area of the rooftop of the building.
The volume of a pyramid is one third of the product of its base area and height.
The surface area of a pyramid is just as important as its volume.
Maya's father decides to cover the roof of their house with waterproof insulation material. Maya's father asks Maya to calculate how many square feet of insulation material is needed.
The roof is a square pyramid with a height of 8 feet and base side length of 30 feet. Help Maya calculate the area.
To find the slant height, use the Pythagorean Theorem. Note that only the lateral area of the pyramid is needed.
Maya needs to calculate the lateral area of the square pyramid. To do so, she first needs to calculate the slant height ℓ of the pyramid, which can be found by using the Pythagorean Theorem.
The height h of the pyramid is the distance between the vertex and the center of the base, and b is half the base side length. Therefore, b=230=15 feet. Since a negative value does not make sense in this context, only the principal root is considered. Therefore, the slant height is 17 feet. Next, the perimeter of the base will be found. Since the base is a square, its perimeter p is 4 times the base side length.The applet shows some right pyramids with different regular polygonal bases. Use the given information to answer the question. If necessary, round the answer to two decimal places.