Answer:
area = 50 cm²
Step-by-step explanation:
To calculate area of the composite figure, divide it into simple shapes (triangles, rectangles, squares...), calculate the area of each shape and add them together.
We can divide the figure into the triangle in the left, rectangle in the middle and another triangle in the right.
Formulas
Area of triangle
[tex]A = \frac{1}{2}bh[/tex]
A ... area of triangle
b ... base
h ... height perpendicular to the base
Area of rectangle
[tex]A = length \times width[/tex]
A ... area of rectangle
Step 1: Calculate areas of simpler shapes.
Area of left triangle:
[tex]A = \frac{1}{2}bh[/tex]
[tex]A_{\text{left}\triangle} = \frac{1}{2} \times 5 \text{ cm} \times 4 \text{ cm}[/tex]
[tex]A_{\text{left}\triangle} = 10 \text{ cm}^2[/tex]
Area of rectangle:
[tex]A = length \times width[/tex]
[tex]A_{\text{rectangle}} = 7 \text{ cm} \times 5 \text{ cm}[/tex]
[tex]A_{\text{rectangle}} = 35 \text{ cm}^2[/tex]
Area of right triangle:
[tex]A = \frac{1}{2}bh[/tex]
[tex]A_{\text{right}\triangle} = \frac{1}{2} \times 2 \text{ cm} \times 5 \text{ cm}[/tex]
[tex]A_{\text{right}\triangle} =5 \text{ cm}^2[/tex]
Step 2: Add the areas together.
[tex]A = A_{\text{left}\triangle} + A_{\text{rectangle}} + A_{\text{right}\triangle}[/tex]
[tex]A = 10 \text{ cm}^2 + 35 \text{ cm}^2 + 5 \text{ cm}^2[/tex]
[tex]A = 50 \text{ cm}^2[/tex]
