Find the area of isosceles triangle parameter is 31cm and it base is 12cm
Answers
Answer:
See a solution process below:
Explanation:
The formula for the area of a triangle is:
A
=
1
2
b
h
The base of this isosceles triangle is given as 12cm.
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Because the line which bisects and isosceles triangles is at a right angle to the base we can use the Pythagorean Theorem to find the height.
The Pythagorean Theorem states:
a
2
+
b
2
=
c
2
Where:
a
and
b
are sides of a right triangle.
c
is the hypotenuse of a right triangle.
In this problem, the hypotenuse, or
c
, is
20
cm
One side of the right triangle is the height which we need to solve for.
The other side of the right triangle for this isosceles triangle is
1
2
of the base, or,
6
cm
Substituting and solving for
a
gives:
a
2
+
(
6
cm
)
2
=
(
20
cm
)
2
a
2
+
36
cm
2
=
400
cm
2
a
2
+
36
cm
2
−
36
cm
2
=
400
cm
2
−
36
cm
2
a
2
+
0
=
364
cm
2
a
2
=
364
cm
2
√
a
2
=
√
364
cm
2
a
≅
19
cm
Therefore the height is approximately: 19.08cm
We can now substitute into the formula for the area to determine the area of this triangle:
A
=
1
2
×
12
cm
×
19
cm
A
=
6
cm
×
19
cm
A
=
114
cm
2
accurate to the nearest square centimeter