Look at Δ
ABD in Figure
1 . If a line
BC
is drawn through
B parallel to
AD
and another line
DC
is drawn through
D parallel to
AB
, then you will have formed a parallelogram.
BD
is now a diagonal in this parallelogram. Because a diagonal divides a parallelogram into two congruent triangles, the area of Δ
ABD is exactly half the area of
ABCD.
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Figure 1
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Area of a triangle is half the area of the associated parallelogram.
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Finding the Area
Because
Aparallelogram =
bh, then
Finding the Perimeter
In Δ
ABD (Figure
1 ), the perimeter is found simply by adding the lengths of the three sides.
Example 1: Find the perimeter and area for the triangles in Figures
2 (a), (b), and (c).
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Figure 2
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Finding perimeters and areas of triangles.
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Example 2: If the area of a triangle is 64 cm2 and it has a height of 16 cm, find the length of its base.
Multiply both sides by 2.
The triangle will have a base of 8 centimeters.
Fundamental Ideas
Perimeter and Area
