Question
A triangle has a base of $13.9\text{ cm}$ and a height of $11.3\text{ cm}$. What is the area of the triangle ?
The correct answer is
$78.53\text{ cm}^2$
Calculating Triangle Area
To find the area of a triangle, we use the formula:
$Area = \frac{1}{2} \times \text{base} \times \text{height}$
Applying the Formula
Given:
- Base = $13.9\text{ cm}$
- Height = $11.3\text{ cm}$
Substitute the values into the formula:
$Area = \frac{1}{2} \times 13.9\text{ cm} \times 11.3\text{ cm}$
Step-by-Step Calculation
- Multiply the base by the height: $13.9 \times 11.3 = 157.07$
- Divide the result by 2 (or multiply by $\frac{1}{2}$): $\frac{157.07}{2} = 78.535$
The calculated area is $78.535\text{ cm}^2$. This value is closest to option D.
Final Answer Verification
The calculated area is approximately $78.53\text{ cm}^2$. Comparing this with the given options:
- Option A: $72.63\text{ cm}^2$
- Option B: $77.73\text{ cm}^2$
- Option C: $75.43\text{ cm}^2$
- Option D: $78.53\text{ cm}^2$
Option D matches the calculated area, considering potential rounding.
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Important Questions from Mensuration 2D (Notes)
- A 2 cm wide wooden strip is to be fixed on a photo of 40 cm x 30 cm size all along its four sides. What is the minimum length of the wooden strip required?
- $110$ मी. $\times 60$ मी. घास-आच्छादित आयताकार प्लॉट के अंदर चारों ओर $2$ मी. चौड़ा बजरी का रास्ता बनाना है। $₹2$ प्रति वर्ग मी. की दर से बजरी बिछाने का लागत ज्ञात कीजिए।
- The perimeter of a square is $596$ m. Its area (in m$^2$) is:
- A hollow spherical shell is made of a metal of density 4 g/cm$^3$. Its internal and external radius are 15 cm and 18 cm, respectively. What is the weight (in kg) of the shell?
(Use $\pi = \frac{22}{7}$ and Density = $\frac{\text{Mass}}{\text{Volume}}$) - Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 4 metres per second into a cylindrical tank, the radius of whose base is 80 cm. By how much will the level of water rise in 16 minutes?
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