# The lateral edges of a regular quadrangular pyramid are 2.5, and the apothem

The lateral edges of a regular quadrangular pyramid are 2.5, and the apothem of the lateral face is 2. Find the area of the lateral surface of this pyramid.

The apothem of a regular quadrangular pyramid divides the side face into two identical right-angled triangles. Apothema – leg, lateral rib – hypotenuse.

Find the second leg of this right-angled triangle.

a = √ ((2.5 cm) ² – (2 cm) ² = √2.25 cm² = 1.5 cm.

Now let’s find the area of this right-angled triangle.

St = 2 cm * 1.5 cm ÷ 2 = 1.5 cm².

On one side face there are 2 such triangles, on the entire side face there are 8 such triangles.

S = 1.5 cm² * 8 = 12 cm².

Answer: the area of the lateral surface of the pyramid is 12 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.