The sides of a triangle are 7 cm, 24 cm, and 25 cm. What is the area of this triangle?
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.
Important Questions from Mensuration
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
