Class 9 Area Theorems (Parallelograms and Triangles) Mock Test (ICSE)

Topics in Area Theorems (Parallelograms and Triangles)

• Parallelograms on the same base and between the same parallels
• Triangles on the same base and between the same parallels
• Median divides a triangle into two equal areas
• Problems on area theorems

Area Theorems (Parallelograms and Triangles) practice questions with answers

1. Q1Multiple choice·1 mark
   If $\triangle ABC$ and $\triangle DBC$ are on the same base $BC$ and on the same side of $BC$ such that $\text{area}(\triangle ABC) = \text{area}(\triangle DBC)$, then:

   1. (a)$AD \perp BC$
   2. (b)$AD \parallel BC$
   3. (c)$BD = CD$
   4. (d)$AB = AC$
   Show answer and step marks

   1. Correct option: (b) $AD \parallel BC$. Triangles on the same base and equal in area lying on the same side of the base lie between the same parallels, hence $AD \parallel BC$.+1

   Answer: (b)
2. Q2Multiple choice·1 mark
   If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is:

   1. (a)$1 : 1$
   2. (b)$2 : 1$
   3. (c)$1 : 2$
   4. (d)$1 : 4$
   Show answer and step marks

   1. Correct option: (c) $1 : 2$. The area of a triangle is half the area of a parallelogram on the same base and between the same parallels, so the ratio is $1 : 2$.+1

   Answer: (c)
3. Q3Multiple choice·1 mark
   In $\triangle PQR$, $M$ is the midpoint of side $QR$. If the area of $\triangle PQR$ is $56\text{ cm}^2$, then the area of $\triangle PMR$ is:

   1. (a)$112\text{ cm}^2$
   2. (b)$14\text{ cm}^2$
   3. (c)$56\text{ cm}^2$
   4. (d)$28\text{ cm}^2$
   Show answer and step marks

   1. Correct option: (d) $28\text{ cm}^2$. A median divides a triangle into two triangles of equal areas. Thus, $\text{area}(\triangle PMR) = \frac{1}{2} \times 56\text{ cm}^2 = 28\text{ cm}^2$.+1

   Answer: (d)
4. Q4Multiple choice·1 mark
   If two parallelograms are on the same base and between the same parallels, then the ratio of their areas is:

   1. (a)$1 : 1$
   2. (b)$2 : 1$
   3. (c)$1 : 4$
   4. (d)$1 : 2$
   Show answer and step marks

   1. Correct option: (a) $1 : 1$. Parallelograms on the same base and between the same parallels are equal in area, so their ratio is $1 : 1$.+1

   Answer: (a)

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