The problem asks to find the total area of a composite shape consisting of a right triangle and a rectangle. The base of the triangle is given as $12$ km and its height is given as $10$ km. The rectangle has sides of $10$ km and $10$ km. We are given the formulas for the area of a rectangle and a triangle as hints.

1. Problem Description

The problem asks to find the total area of a composite shape consisting of a right triangle and a rectangle. The base of the triangle is given as $12$ km and its height is given as $10$ km. The rectangle has sides of $10$ km and $10$ km. We are given the formulas for the area of a rectangle and a triangle as hints.

2. Solution Steps

First, we find the area of the rectangle. The area of a rectangle is given by the formula:

$Area_{rectangle} = base \times height$

In this case, the base is $10$ km and the height is $10$ km. Therefore,

$Area_{rectangle} = 10 \text{ km} \times 10 \text{ km} = 100 \text{ km}^2$

Next, we find the area of the triangle. The area of a triangle is given by the formula:

$Area_{triangle} = \frac{1}{2} \times base \times height$

In this case, the base is $12$ km and the height is $10$ km. Therefore,

$Area_{triangle} = \frac{1}{2} \times 12 \text{ km} \times 10 \text{ km} = 6 \text{ km} \times 10 \text{ km} = 60 \text{ km}^2$

Finally, we add the area of the rectangle and the area of the triangle to find the total area:

$Area_{total} = Area_{rectangle} + Area_{triangle} = 100 \text{ km}^2 + 60 \text{ km}^2 = 160 \text{ km}^2$

3. Final Answer

The total area is $160 \text{ km}^2$.