Three
I hope you want to know the Perimeter. Perimeter is the total length of the boundary of the region bounded by a shape. For a rectangle it is the sum of the 4 bounding sides, or 2*(L+B), where L is Length of the rectangle and B is Breadth of the rectangle. For a Triangle it is the sum of the 3 sides. If you consider an equilateral triangle. By property the 3 sides of an equilateral triangle are equal. Hence the Perimeter of an equilateral triangle is denoted as; 3*a, where a is the length of one of the sides of the triangle. It is possible that the perimeter of a rectangle is same as that of many different types of triangles. We can formulate a relationship for a special case where the perimeter of a rectangle is equal to the perimeter of an equilateral triangle; P(R) = P(ET), P(R) is perimeter of rectangle and P(EQ) is perimeter of Equilateral triangle. P(R)=2(L*B) = P(EQ) = 3*a; hence, a = (2/3)*(L*B) = P(R)/3. i.e., the sides of the Equilateral triangle are one thirds of the perimeter of the rectangle.
The altitude of an equilateral triangle bisects the base. So, if the sides of the triangle were l cm, the altitude forms a right angled triangle with sides h, l/2 and hypotenuse l cm. Then, by Pythagoras, h2 = 3l2 / 4 so that h = l*sqrt(3)/2 and then area = l*h/2 = l*[l*sqrt(3)/2]/2 =l2*sqrt(3)/4
0.5 x base length x vertical height
The area of an equilateral triangle is A=sqrt(3)*(l^2)/4, l is the length and A is the area multiply both sides by 4/sqrt(3) and get 4*A/sqrt(3)=l^2 take the square root of both sides and get l = sqrt(4*A/sqrt(3))
Three
I hope you want to know the Perimeter. Perimeter is the total length of the boundary of the region bounded by a shape. For a rectangle it is the sum of the 4 bounding sides, or 2*(L+B), where L is Length of the rectangle and B is Breadth of the rectangle. For a Triangle it is the sum of the 3 sides. If you consider an equilateral triangle. By property the 3 sides of an equilateral triangle are equal. Hence the Perimeter of an equilateral triangle is denoted as; 3*a, where a is the length of one of the sides of the triangle. It is possible that the perimeter of a rectangle is same as that of many different types of triangles. We can formulate a relationship for a special case where the perimeter of a rectangle is equal to the perimeter of an equilateral triangle; P(R) = P(ET), P(R) is perimeter of rectangle and P(EQ) is perimeter of Equilateral triangle. P(R)=2(L*B) = P(EQ) = 3*a; hence, a = (2/3)*(L*B) = P(R)/3. i.e., the sides of the Equilateral triangle are one thirds of the perimeter of the rectangle.
The altitude of an equilateral triangle bisects the base. So, if the sides of the triangle were l cm, the altitude forms a right angled triangle with sides h, l/2 and hypotenuse l cm. Then, by Pythagoras, h2 = 3l2 / 4 so that h = l*sqrt(3)/2 and then area = l*h/2 = l*[l*sqrt(3)/2]/2 =l2*sqrt(3)/4
0.5 x base length x vertical height
The area of an equilateral triangle is A=sqrt(3)*(l^2)/4, l is the length and A is the area multiply both sides by 4/sqrt(3) and get 4*A/sqrt(3)=l^2 take the square root of both sides and get l = sqrt(4*A/sqrt(3))
For an equilateral triangle, there are three axes of symmetry. A plane figure is symmetrical about the line l if, whenever P is a point of the figure, so too is P', where P' is the mirror-image of P in the line l. The line is called a line of symmetry (or axis of symmetry), and the figure is said to be a symmetrical by the reflection in the line l. An equilateral triangle with reflection symmetry has two halves that are mirror images of each other. If the shape is folded over its line of symmetry, the two halves of the shape match exactly. So, we can say that the two halves of an equilateral triangle are matched exactly only when its shape is folded over the lines of symmetry that passes through their vertixes and the midpoint of its sides. Thus, an equilateral triangle has three lines of symmetry, and three angles of rotation. If you rotate any shape a full turn, it will look like it did before you rotated it. When you rotate a shape less than a full turn about its center point and it looks exactly as it did before you rotated it, it has rotation symmetry. In an equilateral triangle there are three places in the rotation where the triangle will look exactly the same as its starting position. If we turn the triangle one third of a full turn (60 degrees), the vertex 1 will be at position 3, vertex 2 will be at position 1, and vertex 3 will be at position 2, and the triangle will look like its starting position.
Assume regular hexagon of side L. Split the hexagon into 6 equilateral triangles. (A sketch would help here) You need to find the height of the triangle to find it's area. Split the triangle in half with a vertical line. You now have 2 right angle triangles of base L/2 height h. Top angle 30 degrees, bottom angle 60 degrees. L/(2h) = tan 30 h = L/(2tan 30) h = root 3 L/2 Area of 1 equilateral triangle = 1/2 x L x h = (root 3 x L2)/4 Area of hexagon = 6x(root 3 x L2)/4 Area of hexagon = 3x(root 3 x L2)/2
Area of Equilateral Triangle = (Sqrt(3) / 4) * l². So if the length of the triangle is 3, it would be Area = (Sqrt(3) / 4) * l² = (1.73 / 4) * 3² = 0.43 * 9 = 3.87.
A right triangle is equal to 90 degrees. It's like the shape of a capital L.
The altitude/height of an equilateral triangle can be calculated by taking the perpendicular bisector of any side. This line will bisect its opposite angle forming two congruent right angled triangles. The side length of the original equilateral triangle is the hypotenuse and the short leg of right angled triangle is half the hypotenuse. By Pythagoras' Theorem : 42 = 22 + L2.........where L is the length of the altitude. L2 = 42 - 22 = 16 - 4 = 12 L = √12 = 2√3 = 3.464 (3dp)
the angle of elevation from L to K measures 55 degrees. If JK=26,find JL. roind to the nearest tenth
H, I, O, S, X, Z. l as for the shapes circle, square, rectangle, equilateral triangle, any regular polygon (pentagon, hexagon...)