### 12-1 Representations of Three-Dimensional Figures

```12-1 Representations of ThreeDimensional Figures
You identified parallel planes and intersecting
planes in three dimensional figures.
• Draw isometric views of three-dimensional
figures.
• Investigate cross sections of threedimensional figures.
Vocabulary
Isometric view: corner views of three dimensional
objects on two-dimensional paper.
Orthographic drawing: a drawing showing the top,
left, front, and right views of 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.
Step 2 Draw the triangle for the top of the solid.
Step 3 Draw segments 6 units down from each
vertex for the vertical edges.
Step 4 Connect the corresponding vertices. Use
dashed lines for the hidden edges. Shade the
top of the solid.
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.
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.
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.
Which diagram is the correct corner
view of the figure given the
top left fron righ
orthographic drawing?
view view t
t
view view
A.
B.
C.
D.
Cross Section
A cross section: the intersection of a solid and a
plane.
The shape of the cross section formed by the
intersection of a plane and a three-dimensional
figure depends on the angle of the plane.
BAKERY A customer ordered a two-layer sheet cake.
Determine the shape of each cross section of the cake
below.