Find the surface area of the shape below.
1 answer:
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Answer:
Around 5.5 square meters
Step-by-step explanation:
You can start by finding the area of the segment. Since the rest of the circle that is not in the segment is 240 degrees, the segment is 120 degrees or a third of the circle. You can therefore find the area of that segment with the formula square meters. Now, you need to find the area of the triangle inside the sector. This is more difficult than last time, because it is not a 90 degree angle. However, you can solve this by dividing this triangle into two 30-60-90 triangles, which you know how to find the ratio of sides for. In a 30-60-90 triangle, the hypotenuse is twice the length of the smallest leg, and the larger leg is
times larger than the smaller leg. In this case, these dimensions are a base of
for the smaller leg and
for the larger leg, or the base. Using the triangle area formula and multiplying by 2 (because remember, we divided the big triangle in half), you get
square meters. Subtracting this from the area of the segment, you get about 5.5 square meters. Hope this helps!
Answer:
The correct option is;
D(4, 4)
Step-by-step explanation:
The given coordinates of the points are, A(2, 3) B(8, 7), C(6, 1), therefore, the coordinates of the point D that will make CD perpendicular to AB will have a slope = -1/m, where, m = the slope of the line segment AB
The formula for finding the slope, m, of a segment, given the coordinates of two points on the straight line segment (x₁, y₁), (x₂, y₂)
Therefore, for, the segment AB, we have;
m = (7 - 3)/(8 - 2) = 4/6 = 2/3
m = 2/3
Therefore, to make the segment AB perpendicular to the segment CD, the slope of the segment CD will be -1/m = -1/(2/3) = -3/2
The equation of the segment CD in point and slope form is therefore;
y - 1 = -3/2×(x - 6)
y - 1 = -3·x/2 + 9
The standard form of the equation of the segment CD is therefore;
y = -3·x/2 + 9 + 1 = -3·x/2 + 10
y = -3·x/2 + 10
The point that satisfies the above equation is the point (4, 4) because;
4 = -3 × 4/2 + 10
The correct option is therefore, D(4, 4).