The lateral edges of a regular quadrangular pyramid are 2.5, and the apothem
| May 29, 2021 | education
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
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