Math 213
Computer Lab 3
Martian Geometry Formulas
Name_____________________________
Due: May 1,2011
An altitude (height) is perpendicular to the base of a polygon.
Drawing a triangle altitude: On Sketchpad draw a scalene, non-right triangle.
Choose a base and its opposite vertex. In the Construct menu choose
perpendicular. Click off to the side. Select the perpendicular line and the base
of your triangle. Choose your segment tool and connect the original vertex to a
new point at the intersection of your base and the perpendicular line. Using the
Display menu, hide the line (do not hide the line segment!).The remaining
segment is an altitude of your triangle, and it is the height that goes with your
base.
To draw the height on a quadrilateral: Draw the perpendicular between two
parallel lines. Select your base and a point on the opposite side and construct
your height in the same manner as the triangle altitude above.
A mid-segment is the segment midway between a base and its opposing vertex or
the segment midway between two parallel sides.
Drawing a mid-segment of a triangle: Start with a triangle. Choose a side that
is not the base. In the Construct menu choose midpoint. Choose the remaining
side and construct it’s midpoint. Connect these two midpoints with a segment.
You have drawn the mid-segment that goes with the base and height of the
triangle. On a quadrilateral the mid-segment joins the midpoints of opposite
sides.
A diagonal ____________________________________________________________.
Drawing diagonals: Connect vertices with a segment that falls within the interior of the
polygon.
Measuring areas of polygons: To have Sketchpad measure the area of a polygon, first
construct the polygon interior. Select the vertices of your polygon in counterclockwise order,
then from the Construct menu choose “Polygon” interior. Next select your interior, select the
Measure menu and choose area.
Computing measures: You can also use Sketchpad’s calculator to complete formulas and
compute. Once you have measurements displayed on your sketch, choose the Measurement
menu and select calculate. Select the measure(s) from your sketch and use the calculator to
complete computations.
Constructing and measuring an arc length: Construct a circle. Construct two more points on
your circumference. Select these points in counterclockwise order on the arc you wish to
create. Select Construct and you will find arc highlighted. If you wish to hide the rest of your
circle, do so. To measure select your arc and use the Measurement menu.
Your assignment for this week geometers: Determine whether or not the Martian
geometry formulas for areas of each of six polygons work. Use Sketchpad to compute
the area the two ways—our way and the Martian way. Compare the results. If the
Martian formula works, explain how it works. You may do this on your sketch. E-mail
your work. Due next Thursday, April 23.
Martian Geometry
The Martians have developed their own geometric formulas. For each
determine whether they will work on Earth. Explain your answer.
1. On Mars the area of a triangle is
A= s*m where m is the length of a
midsegment and s is the length of
an altitude perpendicular to m.
s
s
m
2. The area of a trapezoid is
given by A = s*m with the
midsegment parallel to the
bases of the trapezoid.
3. The area of a parallelogram
is the same formula.
4. The area of a rectangle and
square are the same as the
triangle and trapezoid.
5. The area of a rhombus is
A = 1/2 * d1 * d2; d1 and d2
are diagonals of the rhombus.
6. The area of a sector is A = ½ r * s
where r is the radius
and s is the arc length.
s
s
s
s
m
m
m and s, take
your pick!