Question

calculate the area of a the triangle whose sides are 18 cm , 24cm and 30cm in length . also ,find the length of a altitude coresponding to the smallest side ​

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Find the semi-perimeter:

p = (18 + 24 + 30) ÷ 2 = 36 cm

Find the area of the triangle:

area = √p(p-a)(p-b)(p-c)

area = √36(36 - 18)(36 - 24)(26 - 30)

area = √46656

area = 216 cm²

Find the length of the altitude corresponding to the smallest side:

area = 1/2 (base) (height)

216 = 1/2 (18) (height)

216 = 9 height

height = 216 ÷ 9 = 24 cm

Answer: The area is 216 cm² and the corresponding height is 24 cm