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Lesson Menu 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 5-Minute Check 1 A.234 units 2 B.346 units 2 C.404 units 2 D.468 units 2 Find the area of a rhombus with diagonals of 18 and 26.

Over Chapter 11 5-Minute Check 1 A.234 units 2 B.346 units 2 C.404 units 2 D.468 units 2 Find the area of a rhombus with diagonals of 18 and 26.

Over Chapter 11 5-Minute Check 2 A.188 units 2 B.142 units 2 C.110 units 2 D.104 units 2 Find the area of a trapezoid with bases of 14 and 30 and height of 5.

Over Chapter 11 5-Minute Check 2 A.188 units 2 B.142 units 2 C.110 units 2 D.104 units 2 Find the area of a trapezoid with bases of 14 and 30 and height of 5.

Over Chapter 11 5-Minute Check 3 A units 2 B units 2 C units 2 D units 2 Find the area of a regular hexagon with side length of 18.

Over Chapter 11 5-Minute Check 3 A units 2 B units 2 C units 2 D units 2 Find the area of a regular hexagon with side length of 18.

Over Chapter 11 5-Minute Check 4 A.648 units 2 B.527 units 2 C.437 units 2 D.324 units 2 Find the area of a square with apothem length of 9.

Over Chapter 11 5-Minute Check 4 A.648 units 2 B.527 units 2 C.437 units 2 D.324 units 2 Find the area of a square with apothem length of 9.

Over Chapter 11 5-Minute Check 5 A.82.3 units 2 B.97.4 units 2 C units 2 D units 2 Find the area of a regular triangle with side length of 15.

Over Chapter 11 5-Minute Check 5 A.82.3 units 2 B.97.4 units 2 C units 2 D units 2 Find the area of a regular triangle with side length of 15.

Over Chapter 11 5-Minute Check 6 A.21.3 ft 2 B.72 ft 2 C.108 ft 2 D.32 ft 2 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

Over Chapter 11 5-Minute Check 6 A.21.3 ft 2 B.72 ft 2 C.108 ft 2 D.32 ft 2 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

CCSS 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.

Then/Now 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.

Vocabulary isometric view cross section

Example 1 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 1Mark the corner of the solid, then draw segments 6 units down, 6 units to the left, and 4 units to the right.

Example 1 Use Dimensions of a Solid to Sketch a Solid Step 2Draw the triangle for the top of the solid.

Example 1 Use Dimensions of a Solid to Sketch a Solid Step 3Draw segments 6 units down from each vertex for the vertical edges.

Example 1 Use Dimensions of a Solid to Sketch a Solid Step 4Connect the corresponding vertices. Use dashed lines for the hidden edges. Shade the top of the solid. Answer:

Example 1 Use Dimensions of a Solid to Sketch a Solid Step 4Connect the corresponding vertices. Use dashed lines for the hidden edges. Shade the top of the solid. Answer:

Example 1 Which diagram shows a rectangular prism 2 units high, 5 units long, and 2 units wide? A.B. C.D.

Example 1 Which diagram shows a rectangular prism 2 units high, 5 units long, and 2 units wide? A.B. C.D.

Example 2 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.

Example 2 Use Dimensions of a Solid to Sketch a Solid The front view indicates that there are four standing 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 fourth column to the far right is 1 block high. The dark segments 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.

Example 2 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 dot paper to represent the edges of the solid. Answer:

Example 2 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 dot paper to represent the edges of the solid. Answer:

Example 2 Which diagram is the correct corner view of the figure given the orthographic drawing? A.B. C.D. top view left view front view right view

Example 2 Which diagram is the correct corner view of the figure given the orthographic drawing? A.B. C.D. top view left view front view right view

Example 3 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.

Example 3 Identify Cross Sections of Solids Answer:

Example 3 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:

Example 3 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?

Example 3 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?

End of the Lesson