Question 15

Explanation

Given that triangle $ABC$ is similar to triangle $ADE$.

From the visualization, we can see the coordinates of the points as follows:

• $A(2, 1)$
• $B(8, 4)$
• $C(8, 1)$
• $E(2, -3)$
• $D(10, 1)$ (approximate from the diagram)

Calculating Side Lengths

For triangle $ABC$, which is a right triangle at $C$:

For triangle $ADE$:

Using Similarity

Since both triangles are similar, the ratios of corresponding sides are equal.

Substitute the known values:

Multiply both sides by $6$:

Calculating the Area of Triangle ADE

Both triangles have right angles (triangle ABC at C, triangle ADE at A).

The area of a right triangle can be calculated using the formula:

For triangle $ADE$:

Therefore, the area of triangle $ADE$ is $16$.