Question

1. mp modeling real life a paperweight is shaped like a triangular pyramid. find the surface area of the paperweight.

Explanation:

Step1: Identify the base and lateral faces

The triangular pyramid (tetrahedron) has a triangular base with base \( b = 2 \) in and height \( h_{base}=1.7 \) in, and three congruent triangular lateral faces with base \( b = 2 \) in and slant height \( l = 2.2 \) in.

Step2: Calculate the area of the base

The area of a triangle is \( A=\frac{1}{2}bh \). For the base:
\( A_{base}=\frac{1}{2}\times2\times1.7 = 1.7 \) square inches.

Step3: Calculate the area of one lateral face

For a lateral triangular face: \( A_{lateral}=\frac{1}{2}\times2\times2.2 = 2.2 \) square inches.

Step4: Calculate the total area of the three lateral faces

Since there are three congruent lateral faces: \( A_{lateral\ total}=3\times2.2 = 6.6 \) square inches.

Step5: Calculate the total surface area

The surface area \( SA \) of the triangular pyramid is the sum of the base area and the total lateral face area:
\( SA = A_{base}+A_{lateral\ total}=1.7 + 6.6 = 8.3 \) square inches.

Answer:

The surface area of the paperweight is \(\boldsymbol{8.3}\) square inches.