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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 3 · Set 2 · Q37
There is a triangular park in the society. The park is divided into two sections as shown in the figure. In the region OAC, children are allowed to…
There is a triangular park in the society. The park is divided into two sections as shown in the figure.
In the region OAC, children are allowed to play games like cricket, football, while in the region AOB, activities which involve running are not allowed. The vertices of the triangular park ABC are A$\displaystyle (0, 4)$, B$\displaystyle (- 2, 0)$ and C$\displaystyle (3, 0)$. Based on the above information, answer the following questions :
(i)
Write the equation of the boundary line AB of the park.
(ii)
Write the equation of the boundary line AC of the park.
(iii)
(a)
Using integration, find the area of region OAC, in which children are allowed to play cricket, football.
OR
(b)
Using integration, find the area of region AOB.
Marking-scheme solution
(i)
Equation of the boundary line AB is $\displaystyle 2 x-y+4=0$
(ii)
Equation of the boundary line AC is $\displaystyle 4 x+3 y=12$
(iii)
(a)
Area of region OAC $\displaystyle =\int_{0}^{3} \dfrac{12-4 x}{3}\, d x$
$\displaystyle =\dfrac{1}{3}\left[12 x-2 x^{2}\right]_{0}^{3}=6$
OR
(b)
Area of region AOB $\displaystyle =\int_{-2}^{0}(2 x+4)\, d x$
$\displaystyle =\left[x^{2}+4 x\right]_{-2}^{0}=4$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.