A. Area of a right triangle with perpendicular and base of 7 and 10 cms respectively is 35 cm$^2$
B. Area of a square with a side measuring 12 cm is 140 cm$^2$
C. Area of a rectangle with sides 11 cm and 70 cm is 770 cm$^2$
D. Area of circle with diameter 28 cm is 606 cm$^2$
E. Area of a circle with radius 7 cm is 154 cm$^2$
Choose the correct answer from the options given below :
Evaluating Solution Statements
We need to verify the area calculations for each shape mentioned in the options.
Statement A: Right Triangle Area
The area of a right triangle is calculated using the formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$.
- Given: base = 10 cm, height = 7 cm
- Calculation: Area = $\frac{1}{2} \times 10 \text{ cm} \times 7 \text{ cm} = 35 \text{ cm}^2$
- Conclusion: Statement A is correct.
Statement B: Square Area
The area of a square is calculated using the formula: Area = side$^2$.
- Given: side = 12 cm
- Calculation: Area = $(12 \text{ cm})^2 = 144 \text{ cm}^2$
- Conclusion: Statement B claims the area is 140 cm$^2$, which is incorrect.
Statement C: Rectangle Area
The area of a rectangle is calculated using the formula: Area = length $\times$ width.
- Given: sides = 11 cm and 70 cm
- Calculation: Area = $11 \text{ cm} \times 70 \text{ cm} = 770 \text{ cm}^2$
- Conclusion: Statement C is correct.
Statement D: Circle Area (Diameter)
The area of a circle is calculated using the formula: Area = $\pi r^2$. First, find the radius from the diameter. Diameter = 28 cm, so radius $r = \frac{\text{Diameter}}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm}$. Using $\pi \approx \frac{22}{7}$.
- Calculation: Area = $\frac{22}{7} \times (14 \text{ cm})^2 = \frac{22}{7} \times 196 \text{ cm}^2 = 22 \times 28 \text{ cm}^2 = 616 \text{ cm}^2$
- Conclusion: Statement D claims the area is 606 cm$^2$, which is incorrect.
Statement E: Circle Area (Radius)
The area of a circle is calculated using the formula: Area = $\pi r^2$. Using $\pi \approx \frac{22}{7}$.
- Given: radius = 7 cm
- Calculation: Area = $\frac{22}{7} \times (7 \text{ cm})^2 = \frac{22}{7} \times 49 \text{ cm}^2 = 22 \times 7 \text{ cm}^2 = 154 \text{ cm}^2$
- Conclusion: Statement E is correct.
Identifying the Correct Option
The correct statements are A, C, and E.
Checking the options provided:
- Option 1: B, C and D only (Incorrect)
- Option 2: B, D and E only (Incorrect)
- Option 3: A, D and E only (Incorrect)
- Option 4: A, C and E only (Correct)
Therefore, the option that includes all the correct statements (A, C, and E) is the right choice.
Important Questions from Mensuration 2D (Notes)
- Find the area of a quadrilateral ABCD whose area is twice the area of a triangle PQR. The sides of triangle PQR are in the ratio 4:5:6 and the perimeter of the triangle is 90 cm (use $\sqrt{7} = 2.6$).
- Find the area of a regular hexagon whose side measures $14\sqrt{3}$ cm.
The difference between two parallel sides of a trapezium is 9 cm. The perpendicular distance between them is 52 cm. If the area of the trapezium is 988 \(cm^2\), find the lengths of the parallel sides (in cm).
- $P_1$ and $P_2$ are two regular polygons. The sum of all the interior angles of $P_1$ is $1800^\circ$. Each interior angle of $P_2$ exceeds its exterior angle by $120^\circ$. The difference between the number of sides of $P_1$ and $P_2$ is:
- The perimeter of the triangle is 24 cm and if the sides of the triangles are by prime numbers then the half of the area of triangle (in $cm^2$) is:
