Find the area of the irregular figure.
A figure with 6 sides is shown.
The lower left edge of the figure measures 4 units.
The lower right edge of the figure measures 15 units. A dashed segment from the top vertex to the bottom edge measures 25 units and meets the bottom edge at right angles. The segment between the left edge and dashed segment measures 16 units. The segment between the dashed segment and right edge measures 10 units.
A.
432 units2
B.
438 units2
C.
650 units2
D.
864 units2
use brain.ly to actually get answers. all you hafta do it just skip the add by adjusting the time on the bottom of the screen to see.
you can always break it up into triangles and maybe rectangles.
The above description is hard to envision.
Why not label the vertices ABCDEF and tell whether it is concave or convex, and what the side lengths are, as wll as any points of intersection.
Huh?
To find the area of the irregular figure, we can break it down into simpler shapes and calculate their individual areas.
First, let's start by identifying the shapes in the figure. We can see that it consists of a triangle and a trapezoid.
The triangle is formed by the dashed segment from the top vertex to the bottom edge, and the two sides of the figure. We can find the area of this triangle using the formula:
Area of a triangle = 1/2 x base x height.
The base of the triangle is the lower right edge of the figure, which measures 15 units. The height of the triangle is the dashed segment from the top vertex to the bottom edge, which measures 25 units.
Therefore, the area of the triangle is:
Area of triangle = 1/2 x 15 units x 25 units = 187.5 units².
Next, let's find the area of the trapezoid. The trapezoid is formed by the two sides of the figure, the bottom edge, and the dashed segment. We can find the area of a trapezoid using the formula:
Area of a trapezoid = 1/2 x (sum of the bases) x height.
The bases of the trapezoid are the lower left edge of the figure, which measures 4 units, and the lower right edge of the figure, which measures 15 units. The height of the trapezoid is the segment between the left edge and the dashed segment, which measures 16 units.
Therefore, the area of the trapezoid is:
Area of trapezoid = 1/2 x (4 units + 15 units) x 16 units = 19.5 x 16 units = 312 units².
Finally, to find the area of the entire irregular figure, we add the areas of the triangle and trapezoid:
Area of the irregular figure = Area of triangle + Area of trapezoid
= 187.5 units² + 312 units²
= 499.5 units².
Therefore, the closest option given is 438 units² (option B).