Question

find the area of the composite figure that contains triangles. 6 km 2 km 34 34 2 km 6 km

Explanation:

Step1: Identify the shapes

The composite figure consists of a rectangle and two congruent triangles.

Step2: Calculate area of rectangle

The rectangle has length \( l = 6 \) km and height \( h = 4 \) km (from the dashed lines). Area of rectangle \( A_{rect} = l \times h = 6 \times 4 = 24 \) \( \text{km}^2 \).

Step3: Calculate area of one triangle

Each triangle has base \( b = 4 \) km (wait, no, looking at the diagram: the triangle's height is 2 km? Wait, no, the dashed lines: the triangle has a base? Wait, no, the triangle: the vertical dashed line is 4 km? Wait, no, the diagram shows for the triangle, the height (the dashed horizontal line) is 2 km? Wait, no, let's re-examine. The triangle: the two triangles on the sides. Each triangle: the base (the vertical side) is 4 km? Wait, no, the diagram: the rectangle is in the middle, with length 6 km, and on each side, a triangle. The triangle has a height (the horizontal dashed line) of 2 km, and the vertical side (the base of the triangle) is 4 km? Wait, no, the area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). Looking at the diagram, each triangle: base is 4 km (the vertical side) and height is 2 km (the horizontal dashed line). Wait, no, maybe the triangle's base is 4 km (the vertical length) and height is 2 km (the horizontal length). So area of one triangle: \( \frac{1}{2} \times 4 \times 2 = 4 \) \( \text{km}^2 \).

Step4: Calculate total area of two triangles

Since there are two congruent triangles, total area of triangles \( A_{tri} = 2 \times 4 = 8 \) \( \text{km}^2 \).

Step5: Calculate total area of composite figure

Total area \( A = A_{rect} + A_{tri} = 24 + 8 = 32 \) \( \text{km}^2 \). Wait, wait, no, maybe I messed up the triangle's dimensions. Wait, the rectangle: length 6 km, height 4 km (the vertical dashed line is 4 km). The triangles: each triangle has a base of 4 km? No, the horizontal dashed line for the triangle is 2 km. Wait, no, the triangle: the base is 4 km (the vertical side) and height is 2 km (the horizontal side). Wait, no, area of triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). Let's check the diagram again. The triangle: the two triangles on the sides. Each triangle: the vertical length (the base) is 4 km (from the dashed vertical line: 4 km), and the horizontal length (the height) is 2 km (the dashed horizontal line: 2 km). So area of one triangle: \( \frac{1}{2} \times 4 \times 2 = 4 \). Two triangles: \( 2 \times 4 = 8 \). Rectangle: \( 6 \times 4 = 24 \). Total area: \( 24 + 8 = 32 \) \( \text{km}^2 \). Wait, but let's re-express. Wait, maybe the rectangle is 6 km by 4 km, area 24. Each triangle: base 4 km, height 2 km. So two triangles: 2(0.542)=8. Total 24+8=32. Wait, but maybe I made a mistake in the triangle's base. Wait, the vertical dashed line is 4 km, which is the height of the rectangle, and the horizontal dashed line for the triangle is 2 km. So the triangle: base is 4 km (the vertical side) and height is 2 km (the horizontal side). So area of triangle is 0.542=4. Two triangles: 8. Rectangle: 64=24. Total 32.

Answer:

\( 32 \) square kilometers