1. In the figure for part a, the upper shaded triangle has an area of 1 sauare unit because it is half of a 2-unit by 1-unit rectangle. Similarly, the lower shaded trianglet has an area of 1 % square units because it is half of a 3-unit by 1-unit rectangle. Determine the areas of these figures by subdividing them into squares, halves of squares, and triangles that are halves of rectangles. (Add screenshots of how you divided sections if possible!) а,

Mathematics For Machine Technology
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Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 32A: A piece in the shape of a frustum of a pyramid with regular octagon bases is 23.84 centimeters high....
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The virtual geoboard shown at left in the margin has a rectangular
array of 25 pins around which rubber bands have been placed.
Notice the red polygon on the geoboard is divided into 6 squares
and 7 half squares by blue bands. If one small square serves as a
unit of area, then the total area of the polygon is 9 % unit squares
or 9 ½ square units.
In the following activities you will examine different methods for
determining areas of polygons and discover how the formulas for
the areas of rectangles, parallelograms, and triangles are related.
The unit square for the areas in these activities is the smallest
square with pins at its corners (1 unit by 1 unit), and the area of a
polygon is the number of unit squares needed to cover the
polygon.
1. In the figure for part a, the upper shaded triangle has an area of 1 sguare unit because it is
half of a 2-unit by 1-unit rectangle. Similarly, the lower shaded triangle has an area of 1 %
square units because it is half of a 3-unit by 1-unit rectangle. Determine the areas of these
figures by subdividing them into squares, halves of squares, and triangles that are halves of
rectangles. (Add screenshots of how you divided sections if possible!)
а.
*b.
C.
Area of Figure:
Area of Figure:
Area of Figure:
2+3+1+(1/2)+1+(3/2)
= 9 sq. unit
Transcribed Image Text:The virtual geoboard shown at left in the margin has a rectangular array of 25 pins around which rubber bands have been placed. Notice the red polygon on the geoboard is divided into 6 squares and 7 half squares by blue bands. If one small square serves as a unit of area, then the total area of the polygon is 9 % unit squares or 9 ½ square units. In the following activities you will examine different methods for determining areas of polygons and discover how the formulas for the areas of rectangles, parallelograms, and triangles are related. The unit square for the areas in these activities is the smallest square with pins at its corners (1 unit by 1 unit), and the area of a polygon is the number of unit squares needed to cover the polygon. 1. In the figure for part a, the upper shaded triangle has an area of 1 sguare unit because it is half of a 2-unit by 1-unit rectangle. Similarly, the lower shaded triangle has an area of 1 % square units because it is half of a 3-unit by 1-unit rectangle. Determine the areas of these figures by subdividing them into squares, halves of squares, and triangles that are halves of rectangles. (Add screenshots of how you divided sections if possible!) а. *b. C. Area of Figure: Area of Figure: Area of Figure: 2+3+1+(1/2)+1+(3/2) = 9 sq. unit
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