Given side ratio (smaller to larger) is 4:5.

Here are the solutions to the problems:

24. Two triangles are similar with sides in the ratio 4:5. If the area of the smaller triangle is $64 \text{ cm}^2$, find the area of the larger triangle.

Step 1: Understand the relationship between the ratio of sides and the ratio of areas for similar figures.
If the ratio of corresponding sides of two similar triangles is $a:b$, then the ratio of their areas is $a^2:b^2$.
Given side ratio (smaller to larger) is $4:5$.
So, the area ratio (smaller to larger) is $4^2:5^2 = 16:25$.

Step 2: Set up a proportion using the area ratio and the given area.
Let $A_s$ be the area of the smaller triangle and $A_l$ be the area of the larger triangle.

$$\frac{A_s}{A_l} = \frac{16}{25}$$

Given $A_s = 64 \text{ cm}^2$.

$$\frac{64 \text{ cm}^2}{A_l} = \frac{16}{25}$$

Step 3: Solve for $A_l$.

$$16 \times A_l = 64 \text{ cm}^2 \times 25$$ $$A_l = \frac{64 \times 25}{16} \text{ cm}^2$$ $$A_l = 4 \times 25 \text{ cm}^2$$ $$A_l = \boxed{\text{}100 \text{ cm}^2\text{}}$$

25. Define the term Circle and state the relationship between radius and diameter.
A circle is a set of all points in a plane that are equidistant from a fixed central point.
The relationship between radius ($r$) and diameter ($d$) is that the diameter is twice the radius, or $d = 2r$.

26. Find the circumference of a circle with a radius of $7 \text{ cm}$. ($\pi = \frac{22}{7}$)

Step 1: Use the formula for the circumference of a circle.

$$C = 2\pi r$$

Step 2: Substitute the given values $r = 7 \text{ cm}$ and $\pi = \frac{22}{7}$.

$$C = 2 \times \frac{22}{7} \times 7 \text{ cm}$$ $$C = 2 \times 22 \text{ cm}$$ $$C = \boxed{\text{}44 \text{ cm}\text{}}$$

27. Calculate the area of the following use $\pi = \frac{22}{7}$