Question

A square pyramid is sliced parallel to the base, as shown. What is the area of the resulting two-dimensional cross-section? Square pyramid intersected horizontally by a rectangle. The base of the pyramid measures 10 feet by 10 feet, and the height is 12 feet. The part of the rectangle that intersects the pyramid is a gray square. The square measures 4 feet by 4 feet. A.16 ft² B.40 ft² C.48 ft² D.120 ft²

Answer 1

Answer:

Option A is correct.

Step-by-step explanation:

Given a square pyramid is sliced parallel to the base, we have to find the area of the resulting two-dimensional cross-section.

Square pyramid intersected horizontally by a rectangle. The base of the pyramid measures 10 feet by 10 feet, and the height is 12 feet. The part of the rectangle that intersects the pyramid is a gray square. The square measures 4 feet by 4 feet.

Now, we have to find the area of the resulting two-dimensional cross-section i.e of grey square whose dimensions are 4 feet by 4 feet.

$\text{Area of cross-section=}side\times side=4\times 4=16 ft^2$

Hence, area of resultant cross-section is 16 square feet.

Option A is correct.

Answer 2

There are different ways to calculate the area of the resulting two-dimensional cross-section. The answer is therefore  16 ft²

A pyramid is known to be a polyhedron that is said to have only one base.

Here, all  lateral faces often meet at a vertex found at the top of the pyramid.

Based on its base, the lateral faces can or cannot all be congruent.

When a square pyramid is sliced parallel to the base, there is then an area of the resulting two-dimensional cross-section.

The area of a cross section is = 4 x 4 = 16

Therefore, option A is correct.

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