Question

what is the area of this figure?
3 km
4 km
2 km
2 km
3 km
6 km
4 km
6 km
write your answer using decimals, if necessary.
square kilometers

Explanation:

Step1: Calculate the area of the square

The side length of the square is \(6\) km. The area of a square is \(A = s\times s\), so \(A_1=6\times6 = 36\) square kilometers.

Step2: Calculate the area of the rectangle

The dimensions of the rectangle are \(3\) km (width) and \(4\) km (height). The area of a rectangle is \(A = l\times w\), so \(A_2 = 3\times4=12\) square kilometers.

Step3: Calculate the area of the triangle

The base of the triangle: \(3 + 4+2-(6)=3\) km. The height of the triangle: \(6 - 2=4\) km. The area of a triangle is \(A=\frac{1}{2}\times b\times h\), so \(A_3=\frac{1}{2}\times3\times4 = 6\) square kilometers.

Step4: Calculate the total area

The total area \(A=A_1 - A_2+A_3\). Substitute the values: \(A = 36-12 + 6\).

Answer:

\(30\) square kilometers