Question

1. a net of a regular tetrahedron and its dimensions are shown.

which of the following is true about the regular tetrahedron? select two correct answers.
a. the total surface area can be determined using the expression (3.9)(3)
b. the total surface area can be determined using the expression (7.8)(4).
c. the base is congruent to each face.
d. the tetrahedron has two bases.
e. the total surface area can be determined using the expression (3.9)(4).
use the net to answer questions 3 – 4.
a net of a regular tetrahedron and its dimensions are shown

1. which expression can be used to determine the total surface area of the triangular pyramid?

a. (0.5)(10)(8.7)(4)
b. (0.5)(10)(8.7)(3)
c. (10)(8.7)(4)
d. (10)(8.7)(3)

1. what is the total surface area of the triangular pyramid?

square inches

Explanation:

Question 2

Step1: Calculate 1 triangle area

Area of one equilateral triangle: $\frac{1}{2} \times 3 \times 2.6 = 3.9$ sq ft

Step2: Analyze regular tetrahedron properties

A regular tetrahedron has 4 congruent equilateral triangular faces (so base ≅ each face), total surface area = $3.9 \times 4$.

Step1: Identify face area formula

Area of one triangular face: $\frac{1}{2} \times 10 \times 8.7$

Step2: Total surface area calculation

A triangular pyramid (regular tetrahedron) has 4 congruent faces, so total area = $(0.5)(10)(8.7)(4)$.

Step1: Calculate single face area

$\frac{1}{2} \times 10 \times 8.7 = 43.5$ sq in

Step2: Calculate total surface area

Multiply by 4 faces: $43.5 \times 4 = 174$

Answer:

C. The base is congruent to each face.
E. The total surface area can be determined using the expression (3.9)(4).

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Question 3