Question

what is the area of this figure?

Explanation:

Step1: Calculate the area of the large triangle

The base of the large triangle is \(19\) km. The height of the large triangle is \(8 + 3+3+5=19\) km. The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). So, \(A_1=\frac{1}{2}\times19\times19=\frac{361}{2} = 180.5\) \(km^{2}\).

Step2: Calculate the area of the first rectangle

The first rectangle has dimensions \(4\times3\). Using the formula \(A = length\times width\), \(A_2=4\times3 = 12\) \(km^{2}\).

Step3: Calculate the area of the second rectangle

The second rectangle has dimensions \(3\times3\). Using the formula \(A = length\times width\), \(A_3=3\times3=9\) \(km^{2}\).

Step4: Calculate the area of the third rectangle

The third rectangle has dimensions \(7\times5\). Using the formula \(A = length\times width\), \(A_4=7\times5 = 35\) \(km^{2}\).

Step5: Sum up the areas

The total area \(A=A_1+A_2+A_3+A_4\). \(A=180.5+12 + 9+35\). \(A=236.5\) \(km^{2}\).

Answer:

\(236.5\) \(km^{2}\)