Here is a breakdown of the mathematical problems from the provided image:

Problem 4

In triangle $\triangle ABC$:

• $AB = 5$ cm, $CE = 6$ cm, $AC = 4.8$ cm.
• $BD$ is perpendicular to $AC$.
• Find the area of $\triangle ABC$.

Problem 5

In triangle $\triangle ABC$:

• It is a right triangle with $\angle A = 90^\circ$.
• $AB = 5$ cm, $AC = 12$ cm, $BC = 13$ cm.
• $AD$ is the altitude from $A$ to $BC$.
• Find the length of $AD$.

Problem 6

In quadrilateral $ABCD$:

• $DC = 14$ cm, $BC = 12$ cm.
• The shaded area is to be calculated.

Problem 7

In triangle $\triangle ABC$:

• $BC = 4$ cm, $AC = 8$ cm, and $AE = 3$ cm.
• $D$ lies on $AC$, and $ED$ is perpendicular to $AC$.
• You need to find:
  • (a) The area of triangle $\triangle ABC$.
  • (b) The length of $ED$.

Problem 8

• A triangular field has a base and height in a 4:3 ratio.
• The cost of the field is given as 337.50 rupees, at a rate of 25 rupees per hectare.
• Find the base and height of the triangular field.

Would you like a detailed solution for each of these problems, or is there a specific problem you’d like help with?

Related Questions for Further Practice

1. How do you calculate the area of a triangle given the lengths of its sides?
2. What is the formula to find the area of a right triangle?
3. How do you calculate the altitude in a triangle when the base and area are known?
4. How do you solve problems involving cost per unit area?
5. What is the relationship between area and side ratios in similar triangles?

Tip: When dealing with triangle geometry, remember that altitude can be found using the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$. This helps in calculating unknown altitudes or sides when area is given.