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A traffic signal board, indicating ‘ …

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A traffic signal board, indicating ‘ SCHOOL AHEAD ’ , is an equilateral triangle with side ‛a’ . Find the area of the signal board , using Heron ’s formola . If its perimeter is 180 cm , what will be the area of the signal board?

    • Posted by Rd Pandey 4 years, 2 months ago

    CBSE > Class 09 > Mathematics
    • 2 answers

    Manish Meena 4 years, 2 months ago

    Area of triangle = √(s(s−a)(s−b)(s −c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Given Perimeter = 180 cm Semi-Perimeter = s =Perimeter/2 s = 180/2 s = 90 cm Given that the triangle is equilateral Since all sides of equilateral triangle are equal ∴ a = b = c Perimeter = 180 cm a + a + a = 180 cm 3a = 180 cm a = 180/3 cm a = 60 cm Area of triangle = √(s(s−a)(s−b)(s −c)) Putting a = b = c = 60 cm , s = 90 cm Area of signal board = √(90(90−60)(90−60)(90 −60)) = √( 90(30)(30)(30) ) = √( (9×3×3×3)×(10)4) = √((9×9)×3×(10)4) = √((92)×3×(10)4) = √92×√3 × √((10)4) = 9×√3 ×(〖104)〗^(1/2) = 9 ×√3 × (102) = 9 × 100 × √3 = 900√3 Thus, Area = 900√3 cm2

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    Silviya Shrivastav 4 years, 2 months ago

    S=60+60+60/2 =90 Area=√90(90-60)(90-60)(90-60) =√90*30*30*30 =√3*3*10*30*30*3*10 =3*10*30√3 =900√3cm.sq HOPE IT HELPS

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