Which expressions represent the area of the entire shaded region, including the light and dark shading? select three options. 12
1 answer:
A triangle is a polygon. The total area of the figure can be represented by 12a, (6a+b), and 2b cm².
<h3>What is a triangle?</h3>A triangle is a polygon with 3 sides and 3 vertices.
Since the area of a single triangle is a cm², and the shape is formed of 12 triangles, therefore, the area of the 12 triangles will be equal to,
Given that the area of the complete dark portion is b cm², therefore, the area of the 6 triangles with a cm² of area each, and the black portion can be written as,
As the dark portion also consists of 6 triangles with an area of a cm² each and the total sum of this dark area is b cm². Also, the light portion consists of 6 triangles with an area of a cm². Therefore, the total area can be written as,
Thus, the total area of the figure can be represented by 12a, (6a+b), and 2b cm².
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Answer:
1. A
2. D
3. D
Step-by-step explanation:
The standard form of a parabola is
..... (1)
Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.
1. The directrix of a parabola is y=−8 . The focus of the parabola is (−2,−6) .
...(a)
.... (b)
On solving (a) and (b), we get k=-7 and p=1.
Put h=-2, k=-7 and p=1 in equation (1).
Therefore option A is correct.
2 The directrix of a parabola is the line y=5 . The focus of the parabola is (2,1) .
...(c)
.... (d)
On solving (c) and (d), we get k=3 and p=-2.
Put h=2, k=3 and p=-2 in equation (1).
Therefore option D is correct.
3. The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3 .
...(e)
.... (f)
On solving (e) and (f), we get k=-2.5 and p=0.5.
Put h=0, k=-2.5 and p=0.5 in equation (1).
Therefore option D is correct.