Question

1. find the area of the shape below. break the larger shape into smaller pieces if needed. 9 m diagram of a composite shape with right angles, 14 m, 7 m, 16.1 m 16.1 x 7 = 112.7; 9 + 16.1 / 2 x 7 = 87.85; 112.7 + 87.85 = 200.55

Explanation:

Step1: Identify the two shapes (rectangle and trapezoid)

The figure can be split into a rectangle (length \(16.1\) m, width \(7\) m) and a trapezoid (bases \(9\) m and \(16.1\) m, height \(14 - 7 = 7\) m).

Step2: Calculate area of rectangle

Area of rectangle \(A_{rect} = length \times width = 16.1 \times 7 = 112.7\) \(m^2\)

Step3: Calculate area of trapezoid

Area of trapezoid \(A_{trap} = \frac{(a + b)}{2} \times h\), where \(a = 9\), \(b = 16.1\), \(h = 7\).
\(A_{trap} = \frac{(9 + 16.1)}{2} \times 7 = \frac{25.1}{2} \times 7 = 12.55 \times 7 = 87.85\) \(m^2\)

Step4: Sum the areas

Total area \(A = A_{rect} + A_{trap} = 112.7 + 87.85 = 200.55\) \(m^2\)

Answer:

The area of the shape is \(200.55\) square meters.