An isosceles triangle has congruent sides of 20 cm the base is 10 cm what is the are of the triangle
Use Pythagorean Theorem =
20^2=5^2+x^2 (base is 10 but we will take half so it will be 5)
400= 25+x^2
375=x^2
Take under root
X= 19.36 (height)
Now the Area
1/2bh
1/21019.36
5*19.36
96.8
:-)
The area of the isosceles triangle is 96.82 sq.cm.
"It is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure."
If all the three aides of an isosceles triangle are given then,
\(A=\frac{1}{2}\times b \times \sqrt{a^{2}-\frac{b^{2} }{4} }\)
where b represents the base of an isosceles triangle
'a' represents the length of the congruent sides
For given question,
the length of congruent sides (a) = 20 cm
the base of an isosceles triangle (b) = 10 cm
Using the formula of the area of the isosceles triangle,
\(\Rightarrow A=\frac{1}{2}\times b \times \sqrt{a^{2}-\frac{b^{2} }{4} }\\\\ \Rightarrow A=\frac{1}{2}\times 10 \times \sqrt{(20)^{2}-\frac{(10)^{2} }{4}}\\\\ \Rightarrow A=5 \times \sqrt{400-25}\\\\\Rightarrow A=5\times 19.36\\\\\Rightarrow \bold{A = 96.82}~sq.~cm.\)
Therefore, an area of the isosceles triangle is 96.82 sq.cm.
Learn more about isosceles triangle here:
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