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 23 square units 22 square units 21 square units

Explanation:

Step1: Divide the shapes into known - area figures

We can divide the two - shape combination into triangles and rectangles.

Step2: Calculate the area of each part

For the first shape (left - hand side), we can break it into triangles. Using the formula for the area of a triangle $A=\frac{1}{2}bh$. Counting the base and height from the grid, we find the areas of the triangular parts and sum them up. For the second shape (right - hand side), we also break it into triangles and use the same formula.

Step3: Sum the areas of all parts

After calculating the areas of all individual triangular and rectangular parts of the two shapes, we sum them together.
Let's assume the grid has unit - length squares.
The first shape: We can consider it as composed of two non - overlapping triangles. One triangle with base $4$ and height $3$ has area $A_1=\frac{1}{2}\times4\times3 = 6$. Another triangle with base $4$ and height $3$ has area $A_2=\frac{1}{2}\times4\times3=6$.
The second shape: We can break it into two triangles. One triangle with base $3$ and height $2$ has area $A_3=\frac{1}{2}\times3\times2 = 3$, and another triangle with base $3$ and height $4$ has area $A_4=\frac{1}{2}\times3\times4=6$.
The total area $A=A_1 + A_2+A_3+A_4=6 + 6+3 + 6=21$.

Answer:

21 square units