Page 68 - Calculating Agriculture Cover 20191124 STUDENT - A

5-6 Measurements CH 5]

Explanation: Remember that any number divided by itself is equal to one, thus oz/oz =1;
and any number multiplied by the value 1 equals that number, thus 1 x
805/115 = 805/115 and the resulting division yields a quotient of 7, the
answer.

Areas and Volumes: Geometric Figures

The area of mathematics concentrating on questions of shape, size, relative position of
points and figures, and the properties of space is Geometry. Geometry can deal with flat, two-
dimensional shapes, such as squares and circles which yield areas, or three-dimensional
shapes with depth such as cubes, squares and spheres which yield volume. In geometry a line
is considered to have length but not width or depth. Lines may extend horizontal or vertical,
or obliquely (slanting). Figures composed of lines are geometric figures such as a globe in your
classroom. A plane figure (flat) is any real or imagined surface such as triangles in buildings,
acres of land or water, or navigational points in the air.

Perimeters of Plane Figures
s
The perimeter of a plane figure, such as a rectangle or circle, is that
its boundary is closed. The fence around a field is a perimeter, it can be
measured and the area defined. The total length of the fence can be
measured. Similarly the perimeter of circle as with a barrel or silo (a circle) s s
is closed and can be measured.
If that perimeter is square or rectangular then it consists of 2 equal
lengths and 2 equal widths. If all four sides are equal it is a square and if s
the lengths and widths are unequal the shape is a rectangle. To calculate
the perimeter of a square where S denotes the side length then:
L
P = 4 x s,

To calculate the perimeter of a rectangle, the calculation can be W W
either:

P = 2 x (L + W) or P = 2L + 2W, L

where L is defined as the length and W is defined as the width.

When there is an arithmetic expression such as 2L or 2W the relationship is one of
multiplication and thus 2L means 2 x L, and 2W means 2 x W.
8
Example A: Determine the perimeter of a rectangle that is 8 feet
long and 4 feet wide.
4 4
Solution: P = (2 x 8ft) + (2 x 4ft)
P = 16 ft + 8 ft 8
P = 24 feet

The perimeter of a square is equal to four times the length of one of its
equal length sides (S): 8

P = 4S or P = 4 x S

Example B: Determine the perimeter of a square that is 8 feet long 8 8
on each side.
Solution: P = 4 x 8 = 32 feet 8

The perimeter of a triangle equals the sum of the lengths of the three sides. If the
sides are represented by the letters a, b, and c, the equation is: P = a + b + c

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