In a regular quadrangular pyramid, the height is 6 cm, the lateral rib is 2√21 cm. Calculate the lateral surface area.

| April 25, 2021 | education

In a right-angled triangle MOС, according to the Pythagorean theorem, we determine the length of the leg OС.

OС ^ 2 = CM ^ 2 – OM ^ 2 = 84 – 36 = 48.

OС = √48 = 4 * √3 cm.

Point O divides the AC diagonal in half, then AC = OC * 2 = 4 * √3 * 2 = 8 * √3 cm.

Let’s define the area of ​​the square at the base of the pyramid through its diagonal.

Sb = АС ^ 2/2 = 192/2 = 96 cm2.

Then the side of the base is: AB = BC = √Sbase = √96 = 4 * √6 cm.

The segment OH is the middle line of the triangle ABC, then OH = AB / 2 = 2 * √6 cm.

In the right-angled triangle MOН, according to the Pythagorean theorem, we define the hypotenuse MН.

MH ^ 2 = MO ^ 2 + OH ^ 2 = 36 + 24 = 60.

MH = 2 * √15 cm.

Determine the area of ​​the BCM triangle.

Svcm = BC * MН / 2 = 4 * √6 * 2 * √15 / 2 = 4 * √90 = 12 * √10 cm2.

Then Sside = 4 * Svcm = 48 * √10 cm2.

Answer: The lateral surface area is 12 * √10 cm2.



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