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196 MENSURATION.
To Find the Area of a Parallelogram.
Multiply the length by the width, and the product is the
area.
Note.—The width must not be measured on the slant side,
but perpendicular to its length.
To Find the Area of a Trapezoid.
Add the two parallel sides and divide by two ; multiply the
quotient by the width, and the product is the area. (See Fig. 3).
Example.
Find the area
(Fig. 3).
Solution
:
Area = t_i_? X4 = 32 square feet.
1* » xeei. »•
2
Note.—The correctness of this may be best understood by
assuming the triangle b cut off and placed in the position «
,
and the trapezoid will be changed into a rectangle 8 feet long
and 4 feet wide.
The area of any polygon may be found by dividing it into
triangles and calculating the area of each separately, and the
sum of the areas of all the triangles is the area of the polygon.
Fig. 3.
- 7 feet.
of a trapezoid.
Fig. 4.
The Area of a Circle.
The area of a circle is equal to the square of the radius
multiplied by 3.1-416, which written in a formula is,
Area = 3.1416 r2
.
The area of a circle is also equal to the
square of the diameter multiplied by 0.7854,
which may be written,
Area = 0.7854 d*
The area of a circle is also equal to its
circumference multiplied by the radius and
the product divided by 2, which may be
written,
c X r
2
Area =
The correctness of these formulas may be best understood
by assuming the circle to be divided into triangles (see Fig. 4), of
which the height h = radius and the sum of the bases, 3, of all
the triangles is equal to the circumference of the circle.
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