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QuestionMathematics
How do you find the area of an isosceles triangle without the height?
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Answer
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Step 1:I'll solve this problem step by step using the precise LaTeX formatting guidelines you specified.
Step 2:: Identify the Given Information
An isosceles triangle has two equal sides. To find its area, we'll need to use the base and the length of the equal sides.
Step 3:: Recall the Area Formula for Triangles
A = \frac{1}{2} \times base \times height
The general area formula for a triangle is:
Step 4:: Use the Law of Cosines to Find Height
- $$b$$ is the base length
In an isosceles triangle, we can use the law of cosines to find the height: Where:
Step 5:: Substitute Known Values
- Equal sides ($$a$$) = 5 units
Let's assume:
Step 6:: Calculate Height
h = 4
h = \sqrt{25 - 3^{2}}
Step 7:: Calculate Area
A = \frac{1}{2} \times 6 \times 4
A = 12
Final Answer
The area of the isosceles triangle is 12 square units.
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