Answer:
1,416 cm²
Step-by-step explanation:
There are various lines dividing this figure into shapes, such as rectangles and triangles; this makes it easier to find the area.
- To find the area of a triangle, multiply the base and the height, then multiply the product by 1/2.
- To find the area of a rectangle, multiply the width by the length.
First, find the area of the triangles.
In this figure, there are two triangles with heights of 12 and bases of 18.
[tex]12 * 18 = 216[/tex]
Then, multiply the product by 1/2.
[tex]216 * 1/2 = 108[/tex]
There are two triangles, so multiply, the product, 108, by 2.
[tex]108*2 = 216[/tex]
The area of both combined triangles is 216 cm; the area of a single triangle is 108 cm.
Secondly, find the area of the rectangles.
There are two rectangles with widths of 25 and lengths of 15.
[tex]25*15 = 375[/tex]
There are two rectangles, so multiply the product, 375, by 2.
[tex]375*2 = 750[/tex]
The area of both rectangles combined is 750 cm; the area of a single rectangle is 375 cm.
Lastly, we find the area of the rectangle in the middle.
This rectangle has a length of 18 and a width of 25.
18[tex]18*25 = 450[/tex]
The area of this rectangle is 450 cm.
Lastly, add the areas of all the shapes.
[tex]108 + 108 + 375 + 375 + 450 = 1,416.[/tex]
Therefore, the area of this figure is 1,416 cm².
