A = 1/2 * (a + c) * h
A = 1/2 * (6 + (2 + 6 + 2)) * 6 = 48
Add the areas of two half circles and a trapezoid.
D: Add the areas of a trapezoid and two half circles.
This one is wrong as the figure contains 2 triangles and a rectangle also if proper divisions are drawn. Hence, rest options are true except option D. Option D is incomplete.
D)The areas are equal. A rotation is a rigid transformation, which does not change the size of the original trapezoid. Therefore, the area is preserved.
Rigid transformations are transformations that maintain congruence. They do not change the size or shape of a figure.
Rigid transformations include:
Translations (slide the figure);
Reflections (create a mirror image of the figure);
Rotations (turn the figure).
Since rotations are rigid transformations, this means the measures of all of the sides will be the same; this also means the area will be the same.
D. Rigid transformations were applied therefore not changing any of the shapes values.
they are equal
Ummm you gave the answer already
My first impression is a dog bone standing up on one end.
You're talking about the area of the figure, so I'll think that over
before I look at the choices.
-- 2 semi-circles = 1 whole circle.
-- (1 rectangle) minus (a trapezoid).
Now I'll look through the choices.
A). No good. The trapezoid is cut OUT of the figure,
and shouldn't be added into it.
B). Oh ! Yes ! I didn't look at it that way at first, but
I can see how that works. 'B' is good.
C). and D). Yes. This was my description above.
So 'A' is the method that's wrong.
Lyla made a mistake in Step 3, because she used the wrong dimensions to find the area.
Notice that the base of the triangle is 10 feet, the same as the retangle's. And its height is 6 feet.
So, the area of the triangle would be
And the total area of the composite figure is
Therefore, the right answer is the second choice.