The height of a regular quadrangular pyramid is 8 cm and the side of its base is 12 cm

| September 24, 2021 | education

The height of a regular quadrangular pyramid is 8 cm and the side of its base is 12 cm, calculate: a) the length of the lateral edge b) the total surface area of the pyramid

The pyramid is regular, therefore, at its base there is a square, and the side faces are isosceles triangles.

In triangle СРD we draw the height РН, which, like the median, divides the side DC into equal segments.

Then OH is the middle line of the triangle ACD, and then OH = AD / 2 = 12/2 = 6 cm.

From the right-angled triangle POH, we determine the hypotenuse PH.

PH ^ 2 = PO ^ 2 + OH ^ 2 = 64 + 36 = 100.

PH = 10 cm.

From the right-angled triangle РНD we determine the length РD.

PD ^ 2 = PH ^ 2 + DH ^ 2 = 100 + 36 = 136. PD = PA = PB = PC = √136 = 2 * √34 cm

Answer: The lateral surface area is 3 cm2.

Determine the area of ​​the base of the pyramid. Sbn = AB ^ 2 = 144 cm2.

Let’s define the area of ​​the triangle PDС. Srdc = СD * PH / 2 = 12 * 10/2 = 60 cm2.

Then S side = 4 * Srdc = 4 * 60 = 240 cm2.

S floor = Sb + S side = 144 + 240 = 384 cm2.

Answer: The total area is 384 cm2, the side edge is 2 * √34 cm



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