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Mathematics

Find the area of a triangle whose sides are:

10 cm, 24 cm and 26 cm

Area Trapezium Polygon

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Answer

Let a = 10 cm, b = 24 cm and c = 26 cm.

∵s=a+b+c2=10+24+262=602=30∵ s = \dfrac{a + b + c}{2}\\[1em] = \dfrac{10 + 24 + 26}{2}\\[1em] = \dfrac{60}{2}\\[1em] = 30

∵ Area of triangle = s(s−a)(s−b)(s−c)\sqrt{s(s - a)(s - b)(s - c)}

= 30(30−10)(30−24)(30−26)\sqrt{30(30 - 10)(30 - 24)(30 - 26)} cm2

= 30×20×6×4\sqrt{30 \times 20 \times 6 \times 4} cm2

= 14,400\sqrt{14,400} cm2

= 120 cm2

Hence, area of triangle = 120 cm2.

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