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What is the slant height of a pyramid that has all sides as equilateral triangles with sides of length of 9 cm and the surface area of the pyramid is 140.4 square cm?
The surface area of the pyramid is superfluous to calculating the slant height as the slant height is the height of the triangular side of the pyramid which can be worked out using Pythagoras on the side lengths of the equilateral triangle: side² = height² + (½side)² → height² = side² - ¼side² → height² = (1 - ¼)side² → height² = ¾side² → height = (√3)/2 side → slant height = (√3)/2 × 9cm = 4.5 × √3 cm ≈ 7.8 cm. ---------------------------- However, the surface area can be used as a check: 140.4 cm² ÷ (½ × 9 cm × 7.8 cm) = 140.4 cm² ÷ 35.1 cm² = 4 So the pyramid comprises 4 equilateral triangles - one for the base and 3 for the sides; it is a tetrahedron.
What is the volume of a pyramid with a height of 3 centimeters and a square base with side lengths that measure 8 centimeters?
Volume of pyramid: 1/3*8squared*3 = 64 cubic cm
Prove that a rhombus has congruent diagonals?
Since the diagonals of a rhombus are perpendicular between them, then in one forth part of the rhombus they form a right triangle where hypotenuse is the side of the rhombus, the base and the height are one half part of its diagonals. Let's take a look at this right triangle.The base and the height lengths could be congruent if and only if the angles opposite to them have a measure of 45⁰, which is impossible to a rhombus because these angles have different measures as they are one half of the two adjacent angles of the rhombus (the diagonals of a rhombus bisect the vertex angles from where they are drawn), which also have different measures (their sum is 180⁰ ).Therefore, the diagonals of a rhombus are not congruent as their one half are not (the diagonals of a rhombus bisect each other).
What is the are of a rhombus?
The area of a rhombus can be calculated using the formula ( A = \frac{1}{2} \times d_1 \times d_2 ), where ( d_1 ) and ( d_2 ) are the lengths of the diagonals. Alternatively, if you know the base (b) and height (h), the area can also be calculated as ( A = b \times h ). The area represents the total space enclosed within the rhombus.
What is the height of the triangular faces of a pyramid called?
The height of the triangular face of a pyramid is called the slant height.
What is the formula for the height of a rhombus?
Any formula for the height of a rhombus will depend on the information that you do have. Without that, all that can be said is that, if the sides of the rhombus are x units, then 0 < h < x where the height is h units. If h = 0 then the rhombus degenerates into a flat line, while at h = x it becomes a square.
How do you find the perpendicular height of a square based pyramid?
To find the perpendicular height of a square pyramid, first compute for the volume of the pyramid. Then divide the volume by the area of the base to find pyramid's height.
What is altitude for rhombus?
It is its vertical perpendicular height
Find the surface area of the pyramid. The side lengths of the base are equal?
A pyramid is a generic term used to describe a polyhedron with a polygonal base and triangles rising from that base to meet at an apex. The polygonal base can have any number, n, of sides, provided that n>2. There is, therefore, no information about the number of lateral faces in the pyramid. Also, the surface area of a pyramid depends on its height and there is no information whatsoever about its height. It is, therefore, impossible to answer such an underspecified question.
Volume of a pyrimid?
1/3(b*h) b means the base of the pyramid h means the height of height of the pyramid. The height is not to be confused with the lateral height (Which is the slanted height.) The height is found by drawing a segment from the vertex (or apex) of the pyramid to the center of the base.
What is the area of the rhombus?
The area of a rhombus is calculated by multiplying the base x the vertical height.
Where did the area of a rhombus come from?
If you multiply the lengths of the two diagonals, and divide by 2, you get the area of a rhombus. How does this work: Call the diagonals A & B for clarity. Diagonal A will split the rhombus into 2 congruent triangles. Looking at one of these triangles, its base is the diagonal A, and its height is 1/2 of diagonal B. So the area of one of the triangles is (1/2)*base*height = (1/2)*A*(B/2) = A*B/4. The other triangle has the same area, so the two areas together make up the whole rhombus = 2*(A*B/4) = A*B/2.
