CBQ - Total area of the square planter — task. Maths CBSE Live product, Class 9 (2025-26).

A group of students in a landscape design class are working on a project to create a multi-level garden bed. They need to calculate the areas and volumes of different sections of the garden. One section of the garden is a square planter with sides of length $(a+b+c)$ $units$. Another section of the garden is a raised cubic bed. The side length of this cubic bed is $(a+b)$ $units$. Finally, the students are designing a small, cube-shaped pond. They need to calculate the volume of earth they need to remove. The side length of the pond is $(a-b)$ $units$.

1. Which of the following is the expanded form of the area of the square planter, $((a+b+c)^{2}$?

$a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$a^{2} + b^{2} + c^{2} + a b c$
$a^{2} + b^{2} + c^{2} - a b - b c - c a$
$a^{2} + b^{2} + c^{2} + a b + b c + c a$

2. If $a=4$ $meter$, $b=8$ $meter$ and $c=5$ $meter$, what is the total area of the square planter?

$14$ $\text{meter square}$
$289 meter square$
$49$ $\text{meter square}$
$28$ $\text{meter square}$

3. Which identity can be used to evaluate the volume of the raised cubic bed, $(a+b)^{3}$?

$a^{3} + b^{3} - 3 a b (a + b)$
$(a + b) (a - b)$
$a^{3} + b^{3} + 3 a b (a + b)$
$a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

4. Which identity can be used to evaluate the volume of earth to be removed, $(a-b)^{3}$?

$(a + b) (a - b)$
$a^{3} - b^{3} - 3 a b (a - b)$
$a^{3} - b^{3} + 3 a b (a + b)$
$a^{3} + b^{3} + 3 a b (a + b)$

9. CBQ - Total area of the square planter

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