### Understanding the Net of a Triangular PyramidThe figure below demonstrates a net for a triangular pyramid.![Triangular Pyramid Net](image_url)The net consists of four equilateral triangles merged together to form a larger triangle, where each side of the smaller triangles has specific lengths:- The side length of the outer triangle: 9 ft - The height of each equilateral triangle: 7.79 ft ### Problem StatementGiven that all the triangles in the net are equilateral, calculate the surface area of the pyramid in square feet.### Calculation- **Formula for the area of an equilateral triangle:** \[ A = \frac{\sqrt{3}}{4} \times \text{side}^2 \]- **Number of triangles:** 4 (three faces and the base)To find the surface area of the pyramid, apply the area formula for one equilateral triangle and multiply by 4, then simplify.### Answer BoxAfter performing the calculation, enter your answer in the box below.\[\text{Answer: } A = \boxed{\quad} \text{ ft}^2\]---This explanation helps visualize and understand how to calculate the surface area from the given net of a triangular pyramid. For further practice and variety, ensure to attempt similar problems to strengthen your understanding.

There are totally 4 triangles Given: Height=h= 7.79 ft and the Base=b= 9 ft Formula: Area of a…

Answered: The figure below is a net for a…

The figure below is a net for a triangular рyramid. 7.79 ft 9 ft If all the triangles are equilateral, what is the surface area of the pyramid, in square feet? Answer: A = ft?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter12: Angle Relationships And Transformations

Section12.5: Reflections And Symmetry

Problem 20E

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Concept explainers

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

Question

### Understanding the Net of a Triangular Pyramid

The figure below demonstrates a net for a triangular pyramid.

![Triangular Pyramid Net](image_url)

The net consists of four equilateral triangles merged together to form a larger triangle, where each side of the smaller triangles has specific lengths:

- The side length of the outer triangle: 9 ft
- The height of each equilateral triangle: 7.79 ft

### Problem Statement

Given that all the triangles in the net are equilateral, calculate the surface area of the pyramid in square feet.

### Calculation

- **Formula for the area of an equilateral triangle:**
\[
A = \frac{\sqrt{3}}{4} \times \text{side}^2
\]

- **Number of triangles:**
4 (three faces and the base)

To find the surface area of the pyramid, apply the area formula for one equilateral triangle and multiply by 4, then simplify.

### Answer Box

After performing the calculation, enter your answer in the box below.
\[
\text{Answer: } A = \boxed{\quad} \text{ ft}^2
\]

---

This explanation helps visualize and understand how to calculate the surface area from the given net of a triangular pyramid. For further practice and variety, ensure to attempt similar problems to strengthen your understanding.

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