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An isosceles triangle has two equal sides of length 13 cm each and a base of 10 cm. What is the area of the triangle?
60 cm┬▓
65 cm┬▓
72 cm┬▓
50 cm┬▓
60 cm┬▓
The area of an isosceles triangle can be calculated by dropping a perpendicular from the apex to the base, which bisects the base into two equal segments of 5 cm. Using the Pythagorean theorem, the height h is calculated as 132тИТ52тАЛ=12 cm, which then allows the area to be determined using the standard triangle area formula.
The area of an isosceles triangle can be calculated by dropping a perpendicular from the apex to the base, which bisects the base into two equal segments of 5 cm. Using the Pythagorean theorem, the height h is calculated as 132тИТ52тАЛ=12 cm, which then allows the area to be determined using the standard triangle area formula.
Think of it like splitting a symmetric folded paper tent in half to find the height of the peak relative to the floor.
ABH: Altitude Bisects Half-base
h=s2тИТ(2bтАЛ)2тАЛ тАФ Height of an isosceles triangle with sides s and base b
Area=21тАЛ├Чbase├Чheight тАФ Standard area of a triangle
In an isosceles triangle, the altitude drawn to the base acts as both the median and the perpendicular bisector. This geometry creates two congruent right-angled triangles with a hypotenuse of 13 cm and a base of 5 cm, allowing the use of the theorem a2+b2=c2 to find the altitude h.
The altitude of an isosceles triangle bisects the base.
The Pythagorean theorem is essential for finding unknown dimensions in geometry.
The units of area are always square units, i.e., cm2.
Geometric decomposition simplifies complex shapes into manageable right triangles.
Requires knowledge of base-height relationship; not directly applicable if sides are unknown.
Architectural roof design calculations.
Structural engineering for truss analysis.
The height h is 169тИТ25тАЛ=144тАЛ=12 cm.
Option B, C, and D are incorrect results obtained from miscalculation of the height or incorrect usage of the area formula.
A is correct тАФ The calculated area is 60cm2 using the base of 10 cm and a derived height of 12 cm.
Always verify if a triangle is a Pythagorean triple (like 5, 12, 13) to save time on square root calculations during exams.
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