Question

payton cut out two shapes, as shown, that she will later put together to resemble a house. what is the total area of the two shapes? 20 square units 21 square units 22 square units 23 square units

Explanation:

Step1: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = base\times height\).
From the graph, the base of the parallelogram is \(3\) units and the height is \(3\) units.
\(A_{1}=3\times3 = 9\) square units.

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height.
From the graph, \(a = 2\), \(b = 4\), and \(h = 4\).
\(A_{2}=\frac{(2 + 4)\times4}{2}=\frac{6\times4}{2}=12\) square units.

Step3: Calculate the total area

Add the areas of the two shapes: \(A = A_{1}+A_{2}\).
\(A=9 + 12=21\) square units.

Answer:

21 square units