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If a triangle has sides 6cm, 8cm and 10cm, what is its area?
24┬аsq┬аcm
48┬аsq┬аcm
30┬аsq┬аcm
40┬аsq┬аcm
24┬аsq┬аcm
Recognize that 6,8,10 form a Pythagorean triplet (3:4:5 scaled by 2), which means the triangle is a right-angled triangle with base 6 and height 8 (or vice versa).
Side lengths of the triangle are a=6┬аcm, b=8┬аcm, and c=10┬аcm.
Area=21тАЛ├Чbase├Чheight
Recognize that 6,8,10 form a Pythagorean triplet (3:4:5 scaled by 2), which means the triangle is a right-angled triangle with base 6 and height 8 (or vice versa).
Students often waste valuable time by unnecessarily using Heron's formula instead of recognizing that the given sides form a right-angled triangle.
Identify the Triangle Type
Check if the side lengths satisfy Pythagoras' theorem: 62+82=36+64=100, which equals 102.
62+82=102
Apply Area Formula for Right-Angled Triangle
Since it is a right-angled triangle, the two shorter sides act as the base and height.
Area=21тАЛ├Ч6├Ч8
Calculate the Area
Multiply and divide to find the final area value.
Area=24┬аsq┬аcm
A is correct because the area calculated using the right-angled triangle formula is 24┬аsq┬аcm.
Knowing common Pythagorean triplets like 3тИТ4тИТ5, 5тИТ12тИТ13, and 6тИТ8тИТ10 saves crucial time in both Geometry and Trigonometry sections.
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