A scientist cuts a box parallel to its bases, and the resulting two-dimensional cross section is a square. Which original figure
1 answer:
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*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*
(21)
Area of a Regular Hexagon: square units
(22)
Similar to (21)
Area = square units
(23)
For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:
Hence, area of the hexagon will be: square units
(24)
Given is the inradius of an equilateral triangle.
Substituting the value of inradius and calculating the length of the side of the equilateral triangle:
Side = 16 units
Area of equilateral triangle = square units
Option D: 13 units is the distance between the two points
Explanation:
Given that the points are and
We need to find the distance between the two points.
The distance between the two points can be determined using the distance formula,
Let us substitute the points and
in the above formula, we get,
Simplifying the terms within the bracket, we have,
Adding the terms within the bracket, we get,
Squaring the terms, we have,
Adding, we get,
Simplifying, we have,
Rounding off to the nearest tenth, we get,
Hence, the distance between the two points is 13 units.
Therefore, Option D is the correct answer.