3x+3=90
subtract 3 from both sides
3x=87
divide both sides by 3
x=29
To find IJ, plug in the x value
x+8+x-9
29+8+29-9
57=IJ
This question is nasty. It sounds like you should be finding area of the figure you see. I'll do that first, although I don't think it's the right answer. (But it might be).
Area Trapezoid = (b1 + b2) * h / 2
b1 = 8
b2 = 12
h = 5
Area Trapezoid = (8 + 12 ) * 5 / 2
Area Trapezoid = 20 * 5/2
Area = 50 square feet.
The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5 = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.
Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
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<em>Comment on the geometry</em>
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
2(sv) is the answer for the question
Where is the pic?
i need to see it
