Question
4. Sketch the following: \( \begin{array}{ll}\text { a) a concave hexagon } & \text { b) a convex pentagon } \\ \text { c) a planar figure that is simple but not closed } & \text { d) a kite } \\ \text { e) a non-square rhombus } & \text { f) a right trapezoid }\end{array} \)
Ask by Bond Simmons. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here's how to sketch each figure:
a) **Concave Hexagon**: Draw a six-sided shape with one angle greater than 180 degrees, creating a dent.
b) **Convex Pentagon**: Draw a five-sided shape with all angles less than 180 degrees, making it bulge outward.
c) **Simple but Not Closed Planar Figure**: Draw a continuous line that doesn't intersect itself and doesn't return to the starting point, like a spiral.
d) **Kite**: Draw a four-sided shape with two pairs of adjacent sides equal and one pair of opposite angles equal, resembling a diamond.
e) **Non-Square Rhombus**: Draw a four-sided shape with all sides equal but angles not 90 degrees.
f) **Right Trapezoid**: Draw a four-sided shape with one pair of parallel sides and one non-parallel side perpendicular to the parallel sides, creating a right angle.
If you need more details on any of these, let me know!
Solution
It seems that I am unable to create sketches directly. However, I can describe how to draw each of the requested figures step by step.
### a) Concave Hexagon
1. Start by drawing a hexagon with six sides.
2. Make one of the interior angles greater than 180 degrees, which will create a "dent" in the shape.
3. Ensure that the other angles remain less than 180 degrees.
### b) Convex Pentagon
1. Draw five straight lines to form a pentagon.
2. Ensure that all interior angles are less than 180 degrees, making the shape bulge outward.
### c) Simple but Not Closed Planar Figure
1. Draw a continuous line that does not intersect itself but does not return to the starting point.
2. For example, you can create a spiral or a simple open curve.
### d) Kite
1. Draw two pairs of adjacent sides that are equal in length.
2. The kite should have one pair of opposite angles that are equal.
3. The shape should resemble a diamond or a flying kite.
### e) Non-Square Rhombus
1. Draw a quadrilateral with all sides of equal length.
2. Ensure that the angles are not 90 degrees, making it a rhombus but not a square.
### f) Right Trapezoid
1. Draw a trapezoid with one pair of parallel sides.
2. Ensure that one of the non-parallel sides is perpendicular to the parallel sides, creating a right angle.
If you need further assistance or specific details about any of these shapes, feel free to ask!
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
To make your drawing of a concave hexagon stand out, remember that one of its angles must be greater than 180 degrees, which gives it that unique "caved-in" look. A great trick is to create it by first drawing a regular hexagon and then selecting one of the sides to push inward. For your convex pentagon, ensure that all its interior angles are less than 180 degrees. You can play around with the lengths of the sides; just remember they all connect to form a simple, closed shape. This shape generally looks nice and pointy, like a house!