## Engage NY Eureka Math Grade 6 Module 5 Lesson 16 Answer Key

### Eureka Math Grade 6 Module 5 Lesson 16 Exercise Answer Key

Opening Exercise:

Question 1.
Sketch the faces in the area below. Label the dimensions. Display this graphic using a document camera or other device.

### Eureka Math Grade 6 Module 5 Lesson 16 Exploratory Challenge Answer Key

Exploratory Challenge 1: Rectangular Prisms

a. Use the measurements from the solid figures to cut and arrange the faces into a net. (Note: All measurements are in centimeters.) One possible configuration of rectangles is shown here: b. A juice box measures 4 inches high, 3 inches long, and 2 inches wide. Cut and arrange all 6 faces into a net. (Note: All measurements are in inches.) One possible configuration of faces is shown here: c. Challenge: Write a numerical expression for the total area of the net for part (b). Explain each term in your expression.
Possible answer: 2(2 in. × 3 in.) + 2(2 in. × 4 in.) + 2(3 in. × 4 in.). There are two sides that have dimensions 2 in. by 3 in., two sides that are 2 in. by 4 in., and two sides that are 3 in. by 4 in.

Exploratory Challenge 2: Triangular Prisms

a. Use the measurements from the triangular prism to cut and arrange the faces Into a net. (Note: All measurements are in inches.) One possible configuration of rectangles and triangles is shown here: Exploratory Challenge 3: Pyramids

Pyramids are named for the shape of the base.

a. Use the measurements from this square pyramid to cut and arrange the faces into a net. Test your net to be sure it folds into a square pyramid. One possible configuration of square and triangles is shown below. (Note: all measurements are in centimeters.) b. A triangular pyramid that has equilateral triangles for faces is called a tetrahedron. Use the measurements from this tetrahedron to cut and arrange the faces into a net.
All edges are 4 in. in length. One possible configuration of triangles is shown below. (Note: All measurements are in inches.) ### Eureka Math Grade 6 Module 5 Lesson 16 Problem Set Answer Key

Question 1.
Sketch and label the net of the following solid figures, and label the edge lengths.

a. A cereal box that measures 13 inches high, 7 inches long, and 2 inches wide
One possible configuration of faces is shown below. (Note: all measurements are in inches.) b. A cubic gift box that measures 8 cm on each edge.
One possible configuration of faces is shown here:

All edges are 8 cm in length. c. challenge: Write a numerical expression for the total area of the net in part (b). Tell what each of the terms in your expression means.
6(8 cm × 8 cm) or
(8 cm × 8 cm) + (8 cm × 8 cm) + (8 cm × 8 cm) + (8 cm × 8 cm) + (8 cm × 8 cm) + (8 cm × 8 cm). There are 6 faces in the cube, and each has dimensions 8 cm by 8 cm.

Question 2.
This tent is shaped like a triangular prism. It has equilateral bases that measure 5 feet on each side. The tent is 8 feet long. Sketch the net of the tent, and label the edge lengths. Possible net: Question 3.
The base of a table ¡s shaped like a square pyramid. The pyramid has equilateral faces that measure 25 inches on each side. The base is 25 inches long. Sketch the net of the table base, and label the edge lengths.
Possible net: Question 4.
The roof of a shed is in the shape of a triangular prism. It has equilateral bases that measure 3 feet on each side. The length of the roof is 10 feet. Sketch the net of the roof, and label the edge lengths.   