Question

Ребро правильного тетраэдра равно 4 см. BP=PC. Sdap?

Answer 1

ΔDPA-равнобедренный, DP=PA

DP-высота в равностороннем ΔDBC

DP^2=DB^2-BP^2=4^2-2^2=12

DP=корень из 12

ΔDPA: S=PP1*AD/2

PP1-высота этого равнобедренного Δ

PP1^2=DP^2-PD^2=12-4=8

PP1=корень из 8

S=корень из 8*4/2=2 корня из 8=4 корня из 2

Answer 2

Calculation of Sdap

To calculate the value of Sdap, we need to determine the area of the triangular face of the tetrahedron.

Given that the length of one edge of the tetrahedron is 4 cm and BP = PC, we can assume that the triangle BPC is an equilateral triangle.

To find the area of an equilateral triangle, we can use the formula:

Area = (sqrt(3) / 4) * side^2

where side is the length of one side of the equilateral triangle.

In this case, the side length is 4 cm, so we can substitute it into the formula:

Area = (sqrt(3) / 4) * 4^2

Simplifying the equation:

Area = (sqrt(3) / 4) * 16

Calculating the value:

Area = (1.732 / 4) * 16

Area = 6.928 cm^2

Therefore, the value of Sdap is approximately 6.928 cm^2.

Please note that the provided sources did not directly provide the answer to the question. The calculation of the area of an equilateral triangle is a well-known mathematical formula.