An equilateral triangle and a square have equal perimeters. If the area of the square is 45cm^2, what is the area of the triangle?
The area is [math]20\sqrt{3}[/math] cm[math]^2[/math]. Here’s how to get there:Area of a square: [math]A=s^2[/math], such that A is area and s is side lengthPerimeter of a square: [math]P=4s[/math], such that P is perimeter and s is side lengthPerimeter of an equilateral triangle: [math]P=3b[/math], such that P is perimeter and b is baseArea of a triangle: [math]A=\frac{1}{2}bh[/math], such that A is area, b is base, and h is height. Because the triangle is equilateral, [math]h=\frac{\sqrt{3}}{2}b[/math]Combining these, area of an equilateral triangle: [math]A=\frac{\sqrt{3}}{4}b^2[/math]A square with an area of 45 cm[math]^2[/math] has side lengths of s=[math]\sqrt{45} = 3\sqrt{5}[/math]This means the perimeter of the square is P=[math]4(3\sqrt{5}) = 12\sqrt{5}[/math]The base of an equilateral triangle with the same perimeter is b=[math]\frac{12\sqrt{5}}{3}[/math] = [math]4\sqrt{5}[/math]And the area of this equilateral triangle is A=[math]\frac{\sqrt{3}}{4}(4\sqrt{5})^2 = \frac{\sqrt{3}}{4}(80) = 20\sqrt{3}[/math] cm[math]^2[/math].
If an equilateral triangle has a height of 9 inches, what are the side's lengths?
The height divides it into two right triangles, each with a hypotenuse equal to one side (s), a base which is 1/2s, and then h the height s^2 = (s/2)^2 + h^2 s^2 = s^2/4 + 9^2.............multiply all by 4 4s^2 = s^2 + 324 3s^2 = 324..............divide by 3 s^2 = 108............square rt both sides s = ±10.39........throw out the negative s = 10.39...........answer Proof s^2 = s^2/4 + 9^2 108 = 108/4 + 81 108 = 27 + 81 108 = 108
What is the formula for finding the base or height of an equilateral triangle if you only know the area?
All triangles the Area is: A = 1/2*bh so h = 2A/b An equilateral triangle is no different.The is a formula for the Area in terms of the sides. A = 1/4*s^2√3 so the side is: s = 2√(A/√3)
A bar magnet of magnetic moment M is cut into two parts of equal length. What is the magnetic moment of either part?
If m is magnetic pole strength and 2l is distance between them, the magnetic moment M =2ml.It is clear that cutting the bar magnet in two equal parts ,each half will have magnetic moment =M/2. This is because, cutting the bar magnet in pieces , it's pole strength does not change.( if the cut is perpendicular to the axis of bar magnet.)A solenoid also behaves like a bar magnet. If current I is passing through a solenoid of length l with n turns per unit length and area of cross section ,A, the magnetic moment of the solenoid isM=nl IA.So , cutting this solenoid in two equal halves ,each half will have magnetic moment = M/2.
Can you divide a hexagon into 5 equal pieces?
Yes, the hexagon has equal sides you can divide it into 5 equal shapes as follows: Pick any point on a hexagon and draw a straight line to any SECOND POINT from there (i.e. skip one point in any direction). This will form a triangle. Repeat this process and you will have Three triangles on the outside and one large triangle in the center. Now bisect the large center triangle in the middle. You now have five equal triangles!!
How can I find the perimiter of an equilateral triangle only knowing the area of the equilateral triangle?
area of equilateral triangle(A)= a^2 ..........square root 3 4 20,000=a^2 * square root 3 ................................. 4 80,000=a^2* 1.732 a^2 = 80,000 ............. 1.732 a^2 = 46189.38 approx a=214.92 so perimeter(P)= 4a =4*214.92 =859.68 cm
How do I divide a triangle into 4 equal parts?
In any triangle, the lines connecting the midpoints are parallel to the opposite sides and the four triangles created by these lines and the segments of the original triangle formed by the midpoints are all congruent..Thus, if you need 4 congruent triangles, then you’ll have to partition as follows :Here X, Y and Z are midpoints.However, if equal parts implies equal areas only, instead of congruence, then any triangle can be divided as follows. In the following figure X, Y and Z divide AB into 4 equal parts. The resultant areas of the sub-triangles are same because they share the same height and have equal bases.
Are similar triangles equal in area?
Areas of similar triangles are proportional to the squares on their corresponding sides. If the triangles are congruent then the areas are equal. All congruent triangles are similar. But the converse is not true. So, areas of similar triangles are equal when the triangles are congruent.
What is a two dimensional figure with non congruent side?
Like... a scalene triangle (a triangle with sides of 3 different lengths) is a 2d figure with non congruent sides.
Can two equal triangles be joined to make a rhombus?
If the two equal triangles are isosceles triangle and their are joined to each other at their third unequal sides, we get a rhombus.But if the two equal triangles are isosceles triangle and their are joined to each other at the equal sides, we get a kite.If they are identical scalene triangles and they are joined at their common sides, you get a kite.If the two are isosceles right angled triangle and they are joined to each other at their hypotenuse, we get a rhombus.If the two are right angled triangle and they are joined to each other at their hypotenuse, we get a kite.If the two are right angled triangle and they are joined to each other at the common side other than the hypotenuse, we get a larger triangle.