Math, asked by yuvraj230320, 4 months ago

Find the area of isosceles triangle parameter is 31cm and it base is 12cm

Answers

Answered by s13397ashivangi2258
2

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

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