Question

"Question 8 A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see the given figure). Find the cost of polishing the tiles at the rate of 50p per cm 2 .
Class 9 - Math - Heron's Formula Page 207"

Answer 1

${\bold{\pink{\underline{\green{G}\purple{iv}\orange{en}\red{:-}}}}}$

• First side (a) = 9 cm

• Second side (b) = 28 cm

• Third side (c) = 35 cm

${\bold{\blue{\underline{\red{To}\:\pink{Fin}\green{d}\purple{:-}}}}}$

• cost of polishing the tiles at the rate of 50 p per cm²

${\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

$\bf\:semi\:perimeter=\dfrac{a+b+c}{2}$

$\bf\:semi\:perimeter=\dfrac{9+28+35}{2}$

$\bf\:semi\:perimeter=\dfrac{72}{2}$

$\bf\:semi\:perimeter=36\:cm$

$\bf\boxed\star\purple{\underline{\underline{{Using\:Heron's\:formula:-}}}}$

$\bf\:Area=\sqrt{s(s-a)(s-b)(s-c)}$

$\bf\:Area=\sqrt{36(36-9)(36-28)(36-35)}$

$\bf\:Area=\sqrt{36\times\:27\times\:8\times\:1}$

$\bf\:Area=88.2\:c{m}^{2}(approx)$

Now,

Area of each tile = 88.2 cm²

Area of 16 triangular tiles = 16 × 88.2 cm²

Area of 16 triangular tiles = 1411.2 cm²

then,

Cost of polishing the tile at the rate of 50 p per cm² = ₹ 0.50 × 1411.2

= ₹ 705.60