In the regular quadrangular pyramid sabcd, point r is the middle of the BC edge, s is the vertex.

| June 1, 2021 | education

In the regular quadrangular pyramid sabcd, point r is the middle of the BC edge, s is the vertex. it is known that AB = 1 and sr = 2. Find the total surface area of the pyramid.

Since the pyramid is correct, there is a square at its base.

Let’s determine the area of the base of the pyramid.

Sbn = AB ^ 2 = 1 ^ 2 = 1 cm2.

The side faces of the pyramid are isosceles triangles. Since point R is the middle of the BC, then the segment SR is the median of the triangle SBC, and since SBC is isosceles, then SR is the height of the triangle.

Determine the area of the triangle SBC.

Ssbc = BC * SR / 2 = 1 * 2/2 = 1 cm2.

Then S side = 4 * Ssbc = 4 * 1 = 4 cm2.

The total surface area of the pyramid is equal to: Sпов = Sсн + Side = 1 + 4 = 5 cm2.

Answer: The total surface area of the pyramid is 5 cm2.



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