The height of a regular quadrangular pyramid is 2√2 cm, and the side of the base is 4 cm

| March 9, 2021 | education

The height of a regular quadrangular pyramid is 2√2 cm, and the side of the base is 4 cm: a) find the apothem of the pyramid, b) the lateral surface area

The side faces of a regular pyramid are isosceles triangles.

Let us construct the apothem KН, which is the height and median of the KCD triangle.

Then CH = DH = CD / 2 = 4/2 = 2 cm.

Since point H is the middle of CD, and point O is the middle of AC, the segment OH is the middle line of triangle ACD. Then OH = AD / 2 = 4/2 = 2 cm.

In a right-angled triangle KOH, by the Pythagorean theorem, we determine the length of the hypotenuse KН.

KH ^ 2 = OK ^ 2 + OH ^ 2 = 8 + 4 = 12.

KН = 2 * √3 cm.

Determine the area of ​​the side face of the CDK.

Ssdk = СD * KН / 2 = 4 * 2 * √3 / 2 = 4 * √3 cm2.

The side faces are equal triangles, then: Side = Ssdk * 4 = 16 * √3 cm2.

Answer: The length of the apothem is 2 * √3 cm, the lateral surface area is 16 * √3 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.