Question
The sides of a triangle are 7 cm, 24 cm, and 25 cm. What is the area of this triangle?
The correct answer is
84 cm2
We can use Heron's formula to find the area of the triangle:
Area = √[s(s - a)(s - b)(s - c)],
where s is the semi-perimeter and a, b, and c are the sides of the triangle.
Here, a = 7 cm, b = 24 cm, and c = 25 cm. First, we calculate the semi-perimeter:
s = (7 + 24 + 25) / 2 = 56 / 2 = 28 cm
Now, substitute the values into Heron's formula:
Area = √[28(28 - 7)(28 - 24)(28 - 25)] = √[28 * 21 * 4 * 3] = √[7056] = 84 cm2
The area of the triangle is 84 cm2.
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Important Questions from Mensuration
- The volume of a wall that is 5 times as high as it is broad and 8 times as long as it is high is 12.8 cubic meters. Find the breadth of the wall.
- If the radius of a sphere is increased by 2 cm, then its surface area increases by 704 cm\(^2\). Using \(\pi = \frac{22}{7}\), find the radius of the sphere after the increase.
- What is the perimeter of an equilateral triangle with side 13 cm?
- The perimeter of a square is 76 m. Its area (in $m^2$) is:
- A cylindrical rod has an outer curved surface area of 1800 cm$^2$. If the length of the rod is 52 cm, then the outer radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$
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