The correct option is c.
The area of the figure is
square millimeters.
To find the area of the given figure, which is composed of a triangle and a rectangle, follow these steps:
1. Calculate the area of the rectangle: The area of a rectangle is found by multiplying the length by the width. From the figure, we see that the length is 20 mm and the width is 15 mm. So, the area
is:
![\[ A_{\text{rectangle}} = \text{length} * \text{width} = 20 \, \text{mm} * 15 \, \text{mm} \]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/gcurtvsbsyislbyn03i46o70zvgjjskf0r.png)
2. Calculate the area of the triangle: The area of a triangle is found by using the formula
. The base of the triangle is 20 mm (same as the length of the rectangle) and the height, which is the perpendicular distance from the base to the opposite vertex, is 2 mm. So, the area
is:
![\[ A_{\text{triangle}} = (1)/(2) * \text{base} * \text{height} = (1)/(2) * 20 \, \text{mm} * 2 \, \text{mm} \]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/s8pgznsuneiaqsyk92letvkh1zxjohqy9f.png)
3. Add the areas of the rectangle and triangle to find the total area: The total area
is the sum of
and
.
![\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} \]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/lyr2l6uayybk9rul551lujwshs77ovcav3.png)
Now let's calculate the areas with the given dimensions.
The area of the rectangle is
square millimeters, and the area of the triangle is
square millimeters. Adding these together gives us the total area of the figure:
![\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} = 300 \, \text{mm}^2 + 20 \, \text{mm}^2 = 320 \, \text{mm}^2 \]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/o6q9dmgg2affjk3cqowbryjh628vkjajds.png)
Therefore, the answer is
square millimeters.
The options are give here:
A. 175 square millimeters.
B. 200 square millimeters.
C. 320 square millimeters.
D. 350 square millimeters.