Question

as a land surveyor, you have been hired to find the area of a parcel of land. you have taken all of the appropriate measurements, as shown in the figure. what is the area, in square meters, of this parcel of land?
a 4,500
b 6,400
c 8,000
d 10,400
e 12,800

Explanation:

Step1: Analyze the shape

The parcel of land consists of a rectangle and a right - angled triangle. The rectangle has length \(l = 100\space m\) and width \(w=80\space m\). The right - angled triangle has legs of length \(a = 80\space m\) and \(b = 60\space m\) (we can find the base of the triangle from the rectangle's side, and the height is such that the triangle is right - angled with legs 80m and 60m? Wait, actually, the rectangle has dimensions 100m (height) and 80m (width). The triangle: the two legs are 80m and 60m? Wait, no, let's re - examine. The rectangle: length 100m, width 80m. The triangle: the base of the triangle (the side parallel to the 100m side of the rectangle) is equal to the height of the rectangle? Wait, no, the right - angled triangle has legs of length 80m and 60m? Wait, the area of the rectangle is \(A_{rectangle}=length\times width = 100\times80=8000\space m^{2}\). The area of the right - angled triangle is \(A_{triangle}=\frac{1}{2}\times base\times height\). From the diagram, the base of the triangle is 80m and the height is 60m? Wait, no, the right - angled triangle has legs 80m and 60m? Wait, the hypotenuse is 80m? No, the diagram shows a right - angled triangle with one leg 80m and the other 60m? Wait, no, let's calculate the area of the composite figure.

Wait, the figure is a rectangle plus a right - angled triangle. The rectangle: length \(L = 100\space m\), width \(W = 80\space m\), so area \(A_{1}=100\times80 = 8000\space m^{2}\). The triangle: the two legs of the right - angled triangle are \(a = 80\space m\) and \(b=60\space m\)? Wait, no, the right - angled triangle has legs of length 80m and 60m? Wait, the area of a right - angled triangle is \(A_{2}=\frac{1}{2}\times a\times b\). If \(a = 80\space m\) and \(b = 60\space m\), then \(A_{2}=\frac{1}{2}\times80\times60=2400\space m^{2}\). Then the total area \(A = A_{1}+A_{2}=8000 + 2400=10400\space m^{2}\)? Wait, no, maybe I made a mistake. Wait, the rectangle: 100m (height) and 80m (width). The triangle: the base of the triangle (the side that is attached to the rectangle) is equal to the height of the rectangle? No, wait, the right - angled triangle: one leg is 80m (the same as the width of the rectangle) and the other leg is 60m. Wait, no, let's re - check the dimensions. The rectangle: 100m (vertical side) and 80m (horizontal side). The triangle: the horizontal leg is 80m? No, the right - angled triangle has legs 80m and 60m. Wait, the area of the triangle is \(\frac{1}{2}\times80\times60 = 2400\). Then the total area is \(8000+2400 = 10400\space m^{2}\)? Wait, but the options are A. 4,500; B. 6,400; C. 8,000; D. 10,400; E. 12,800. Wait, maybe I mis - identified the shape. Wait, maybe the rectangle is 80m (height) and 80m (width)? No, the vertical side is 100m. Wait, no, the rectangle has length 100m and width 80m, area \(100\times80 = 8000\). The triangle: the two legs are 80m and 60m? Wait, no, the triangle's area: \(\frac{1}{2}\times80\times60=2400\). Then total area \(8000 + 2400=10400\space m^{2}\).

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l = 100\space m\) and \(w = 80\space m\). So \(A_{rectangle}=100\times80 = 8000\space m^{2}\).

Step3: Calculate the area of the triangle

The formula for the area of a right - angled triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(80\space m\) and the height is \(60\space m\). So \(A_{triangle}=\frac{1}{2}\times80\times60=\frac{1}{2}\times4800 = 2400\space m^{2}\).

Step4: Calculate the total area

The total area of the parcel of land is the sum of the area of the rectangle and the area of the triangle. So \(A = A_{rectangle}+A_{triangle}=8000 + 2400=10400\space m^{2}\).

Answer:

D. 10,400