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Standard XII

Mathematics

Area Method to Find Condition for Co-Linearity

Let the floor...

Question

Let the floor of a hall is covered with identical tiles which are in shape of triangle. One of the triangle has the vertices at $(- 3, 2),$ $(- 1, - 1)$ and $(1, 2) .$ If the floor of the hall is completely covered by $110$ tiles, then the area of the floor (in sq.units) is

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Solution

Given vertices of the triangle are $(- 3, 2), (- 1, - 1)$ and $(1, 2)$

Now, the area of a triangular tile
$= \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} x_{2} & y_{2} x_{3} & y_{3} x_{1} & y_{1} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$

$= \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} - 3 & 2 - 1 & - 1 1 & 2 - 3 & 2 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$

$= \frac{1}{2} | (3 + 2) + (- 2 + 1) + (2 + 6) |$
$= \frac{1}{2} | 12 | = 6$ sq. units

$∴$ Total required area $= 6 \times 110 = 660$ sq. units

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Area Method to Find Condition for Co-Linearity

Standard XII Mathematics

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Let the floor of a hall is covered with identical tiles which are in shape of triangle. One of the triangle has the vertices at (−3,2), (−1,−1) and (1,2). If the floor of the hall is completely covered by 110 tiles, then the area of the floor (in sq.units) is

Let the floor of a hall is covered with identical tiles which are in shape of triangle. One of the triangle has the vertices at $(- 3, 2),$ $(- 1, - 1)$ and $(1, 2) .$ If the floor of the hall is completely covered by $110$ tiles, then the area of the floor (in sq.units) is