Representations of Three-Dimensional Figures LESSON 12–1 Representations of Three-Dimensional Figures

Five-Minute Check (over Chapter 11) TEKS 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 Lesson Menu

Find the area of a rhombus with diagonals of 18 and 26. A. 234 units2 B. 346 units2 C. 404 units2 D. 468 units2 5-Minute Check 1

Find the area of a trapezoid with bases of 14 and 30 and height of 5. A. 188 units2 B. 142 units2 C. 110 units2 D. 104 units2 5-Minute Check 2

Find the area of a regular hexagon with side length of 18. A. 841.8 units2 B. 618.2 units2 C. 420.9 units2 D. 202.5 units2 5-Minute Check 3

Find the area of a square with apothem length of 9. A. 648 units2 B. 527 units2 C. 437 units2 D. 324 units2 5-Minute Check 4

Find the area of a regular triangle with side length of 15. A. 82.3 units2 B. 97.4 units2 C. 106.5 units2 D. 112.7 units2 5-Minute Check 5

Two similar parallelograms have a scale factor of 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 A. 21.3 ft2 B. 72 ft2 C. 108 ft2 D. 32 ft2 5-Minute Check 6

Mathematical Processes G.1(C), G.1(E) Targeted TEKS G.10(A) Identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes. Mathematical Processes G.1(C), G.1(E) TEKS

Draw isometric views of three-dimensional figures. 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. Then/Now

isometric view cross section Vocabulary

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 draw segments 6 units down, 6 units to the left, and 4 units to the right. Example 1

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

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

Use Dimensions of a Solid to Sketch a Solid Step 4 Connect 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

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

The left view indicates that the back left column is 2 blocks high. 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

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

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: 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. Example 3

A. Cut the cone parallel 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? 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. Example 3

Representations of Three-Dimensional Figures LESSON 12–1 Representations of Three-Dimensional Figures