The height of an equilateral triangle is √3/2 x side_length.
So for an equilateral triangle of side length 2a, the area is:
area = 1/2 x base x height
1/2 x (2a) x (√3/2 x 2a)
= √3 a2
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h=2A/b h=heightb=baseA=area
The rule for the volume of a pyramid is:V = 1/3 x Area of base x HeightSo first, we'll find the area of the base.The rule for the Area of a triangle isA = [bcSin(theta)]/2 (you can also use A = 1/2 x base x height.. but that's slower in this case)We know all that it is an equilateral triangle, and because a triangle must have 180 degrees all together, we know that each angle must be 60 degrees.So now we will find the areaA = [bcSin(theta)]/2b and c are both 7, and the angle is 60 degrees so substitute that inA = [7x7sin(60)]/2A = 21.218cm^2Now we know the Area and the Height, so we can find the volume.V = 1/3 x Area of base x HeightSubstitute in our value of 21.218cm^2 for Area and 10cm for heightV = 1/3 x 21.218 x 10V = 70.727 cm^3
Start with simplifying: 2a + -3 = 5 and reordering: -3 + 2a = 5. Then add '3' to each side of the equation: -3 + 3 + 2a = 5 + 3 and you get 2a = 8 once all like terms are combined. The last step is to divide both sides by 2 and you get the answer, which is a = 4.
It's a simple algebraic equation.If the value of 'a' is needed, it can be derived as follows:7a + 10 = 2aSubtract 2a from each side:5a + 10 = 0Subtract 10 from each side:5a = -10Divide each side by 5:a = -2
Since the question is 3(2a), then just write it out. 3(2a) is 2a+2a+2a or 6a.