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tester [92]
3 years ago
12

An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm.

Mathematics
1 answer:
Bas_tet [7]3 years ago
3 0

Answer:

the area of the triangle is 17.4cm^2

Step-by-step explanation:

Finding the area of a triangle

an isosceles triangle has two sides of equal length.

therefore to get the base of the triangle :

we need to subtract the lengths from he perimeter

30-12-12

= 6

<u>the base of the triangle is 6 cm</u>

<u></u>

<h3><u>area of a triangle</u></h3>

formula :

\frac{1}{2} * base * height\\

<h3><u>getting the height of the triangle:</u></h3>

we make use of one side of the triangle , half the base. this creates a right angled triangle

we can make use of the formula

c^{2} = a^{2} + b^{2}

were c is the hypotenuse of 12 cm

a is the adjacent of base (6/2) = 3 cm

and b is the height

12^{2} = 3^{2} +b^{2}

b^{2} = 12^{2} - 3^{2}

b^{2} = 135\\

b = \sqrt{135}

b = 11.6 cm to 3sf

<u>the height is 11.6cm.</u>

<u></u>

<em>area of the triangle is :</em>

1/2 * 3 * 11.6

<u>= 17.4 cm^2</u>

<u />

<u>the area of the triangle is 17.4cm^2</u>

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