In a regular quadrangular pyramid, the side of the base is 6 cm, and the height is 4 cm.

| May 23, 2021 | education

In a regular quadrangular pyramid, the side of the base is 6 cm, and the height is 4 cm. Find the area of the side surface of the pyramid.

The side faces of the pyramid are isosceles triangles.

Let’s construct the height of the PH, which will also be the median of the triangle BСP. Point O divides the diagonal AC in half, then OH is the middle line of the triangle ABC, and then OH = AB / 2 = 6/2 = 3 cm.In the right-angled triangle POH, according to the Pythagorean theorem, we define the hypotenuse PH, which is the height and median of the side face BCP.

PH ^ 2 = PO ^ 2 + OH ^ 2 = 16 + 9 = 25 cm.

PH = 5 cm.

Let us calculate the area of ​​the side face of the BCP. Svsr = BC * PN / 2 = 6 * 5/2 = 15 cm2.

Since the side faces of the regular pyramid are equal, then Sside = 4 * Svav = 4 * 15 = 60 cm2.

Answer: The lateral surface area is 60 cm2.



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