Question : If $\triangle \mathrm{ABC}$ is similar to $\triangle \mathrm{DEF}$ such that $\mathrm{BC}=3 \mathrm{~cm}, \mathrm{EF}=4 \mathrm{~cm}$ and the area of $\triangle \mathrm{ABC}=54 \mathrm{~cm}^2$, then the area of $\triangle \mathrm{DEF}$ is:
Option 1: 78 cm2
Option 2: 96 cm2
Option 3: 66 cm2
Option 4: 44 cm2
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Correct Answer: 96 cm2
Solution : Given, $\triangle \mathrm{ABC}\sim \triangle \mathrm{DEF}$ $\mathrm{BC}=3 \mathrm{~cm}, \mathrm{EF}=4 \mathrm{~cm}$ and the area of $\triangle \mathrm{ABC}=54 \mathrm{~cm}^2$ ⇒ $\frac{area(\triangle{ABC})}{area(\triangle{DEF})}=\frac{BC^2}{EF^2}$ ⇒ $\frac{54}{area(\triangle{DEF})}=\frac{3^2}{4^2}$ ⇒ $\frac{54}{area(\triangle{DEF})}=\frac{9}{16}$ ⇒ $area(\triangle{DEF})=\frac{54\times16}{9}$ ⇒ $area(\triangle{DEF})=96$ cm$^2$ Hence, the correct answer is 96 cm$^2$
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Question : Find out the area of the triangle of base 7 cm and the corresponding height of 12 cm.
Option 1: 42 cm2
Option 2: 54 cm2
Option 3: 43 cm2
Question : The longest side of the obtuse triangle is 7 cm and the other two sides of the triangle are 4 cm and 5 cm. Find the area of the triangle.
Option 1: $1 \sqrt{3} \mathrm{~cm}^2$
Option 2: $6 \sqrt{3} \mathrm{~cm}^2$
Option 3: $3 \sqrt{2} \mathrm{~cm}^2$
Option 4: $4 \sqrt{6} \mathrm{~cm}^2$
Question : The sides of a triangle are 20 cm, 48 cm, and 52 cm. What is the area of the triangle?
Option 1: 320 cm2
Option 2: 480 cm2
Option 3: 560 cm2
Option 4: 245 cm2
Question : The sides of a triangle are 6 cm, 8 cm, and 10 cm. What is the area of the triangle?
Option 1: 20 cm2
Option 2: 28 cm2
Option 3: 24 cm2
Option 4: 16 cm2
Question : The area of a square is 144 cm2. What is the length of each of its diagonals?
Option 1: $14 \sqrt{2} \mathrm{~cm}$
Option 2: $6 \sqrt{2} \mathrm{~cm}$
Option 3: $12 \sqrt{2} \mathrm{~cm}$
Option 4: $12 \mathrm{~cm}$
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