Five-Minute Check (over Chapter 11)

CCSS

Then/Now

New Vocabulary

Example 1:Use Dimensions of a Solid to Sketch a Solid

Example 2:Use an Orthographic Drawing to Sketch a Solid

Example 3:Real-World Example: Identify Cross Sections of Solids

Over Chapter 11

A. 234 units2

B. 346 units2

C. 404 units2

D. 468 units2

Find the area of a rhombus with diagonals of 18 and 26.

Over Chapter 11

A. 188 units2

B. 142 units2

C. 110 units2

D. 104 units2

Find the area of a trapezoid with bases of 14 and 30 and height of 5.

Over Chapter 11

A. 841.8 units2

B. 618.2 units2

C. 420.9 units2

D. 202.5 units2

Find the area of a regular hexagon with side length of 18.

Over Chapter 11

A. 648 units2

B. 527 units2

C. 437 units2

D. 324 units2

Find the area of a square with apothem length of 9.

Over Chapter 11

A. 82.3 units2

B. 97.4 units2

C. 106.5 units2

D. 112.7 units2

Find the area of a regular triangle with side length of 15.

Over Chapter 11

A. 21.3 ft2

B. 72 ft2

C. 108 ft2

D. 32 ft2

Two similar parallelograms have a scale factor

of . The area of the smaller figure is 48 square

feet. What is the area of the larger parallelogram?

__2

3

Content Standards

G.GMD.4 Identify the shapes of two- dimensional cross-sections of three-dimensional objects, and identify three- dimensional objects generated by rotations of two-dimensional objects.

Mathematical Practices

5 Use appropriate tools strategically.

1 Make sense of problems and persevere in solving them.

You identified parallel planes and intersecting planes in three dimensional figures.

• Draw isometric views of three-dimensional figures.

• Investigate cross sections of three- dimensional figures.

• isometric view

• cross section

Use Dimensions of a Solid to Sketch a Solid

Use isometric dot paper to sketch a triangular prism 6 units high, with bases that are right triangles with legs 6 units and 4 units long.

Step 1 Mark the corner of the solid, then drawsegments 6 units down, 6 units to the left, and 4 units to the right.

Use Dimensions of a Solid to Sketch a Solid

Step 2 Draw the triangle for the top of the solid.

Use Dimensions of a Solid to Sketch a Solid

Step 3 Draw segments 6 units down from eachvertex for the vertical edges.

Use Dimensions of a Solid to Sketch a Solid

Step 4 Connect the corresponding vertices. Usedashed lines for the hidden edges. Shade

thetop of the solid.

Answer:

Which diagram shows a rectangular prism 2 units high, 5 units long, and 2 units wide?

A. B.

C. D.

Use an Orthographic Drawing to Sketch a Solid

Use isometric dot paper and the orthographic drawing to sketch a solid.

• The top view indicates one row of different heights and one column in the front right.

Use Dimensions of a Solid to Sketch a Solid

• The front view indicates that there are fourstanding columns. The first column to the left is 2 blocks high, the second column is 3 blocks

high,the third column is 2 blocks high, and the fourthcolumn to the far right is 1 block high. The darksegments indicate breaks in the surface.

• The right view indicates that the front right column

is only 1 block high. The dark segments indicate a

break in the surface.

Use Dimensions of a Solid to Sketch a Solid

• The left view indicates that the back left column is

2 blocks high.

• Draw the figure so that the lowest columns are in

front and connect the dots on the isometric dotpaper to represent the edges of the solid.

Answer:

Which diagram is the correct corner view of the figure given the orthographic drawing?

A. B.

C. D.

top view

leftview

front view

right view

Identify Cross Sections of Solids

BAKERY A customer ordered a two-layer sheet cake. Determine the shape of each cross section of the cake below.

Identify Cross Sections of Solids

If the cake is cut horizontally, the cross section will be a rectangle.

If the cake is cut vertically, the cross section will also be a rectangle.

Answer:

A. Cut the cone parallel to the base.

B. Cut the cone perpendicular to the base through the vertex of the cone.

C. Cut the cone perpendicular to the base, but not through the vertex.

D. Cut the cone at an angle to the base.

A solid cone is going to be sliced so that the resulting flat portion can be dipped in paint and used to make prints of different shapes. How should the cone be sliced to make prints in the shape of a triangle?