0
What else can I help you with?
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.
Surface area of a pyramid?
(1/2 B)h another way is Lateral area + base area. Lateral area is 1/2 perimeter*slant height. You use this if you dont know the height but know the slant. or if you just like to do it this way
How do you get lateral surface area of cube and cuboid?
Lateral surface area of a cuboid = 2 (Length + Breadth) × Height Lateral surface area of a cube = 4 × Side2
What is the lateral surface area of a cylinder with a height of 4cm and a width of 10cm?
A cylinder with a height of 4cm and a width of 10cm has a lateral area of about 125.66cm2
What is the formula for surface area of a pyramid?
Total surface area= 1/2 times the perimeter of the base times the slant height plus the area of the base Lateral surface area= 1/2 times the perimeter times the slant height
What is the height if each lateral face of a pyramid?
The height of each lateral face of a pyramid, often referred to as the slant height, is the distance from the apex (top point) of the pyramid to the midpoint of the base edge of that face. This measurement is crucial for calculating the surface area of the pyramid's lateral faces. The slant height can be determined using the Pythagorean theorem if the vertical height of the pyramid and half the base edge length are known. It is important to differentiate between the vertical height and the slant height when discussing pyramids.
Why is it helpful to know the slant height of a pyramid to find its surface area?
Knowing the slant height helps because it represents the height of the triangle that makes up each lateral face. So, the slant height helps you to find the surface area of each lateral face.
How do you find lateral area of a square pyramid?
You need some information about the height of the pyramid and the formula will depend on whether you have the vertical height or the slant height or the length of a lateral edge.
What is the height of the pyramid 56 cubic centimeters base edge 8 centimeters base height 7 centimeters?
Volume of a pyramid = 1/3*base area*height Height of a pyramid = (3*volume)/base area
Is the lateral edge of a pyramid is also its slant height?
No, the slant height is the from the top vertex to the base of the base of the pyramid, it forms a 90 degree angle with the base and slant height. The lateral edge is literally the lateral (side) edge.
What is the area of a square pyramid lateral sides?
The lateral surface area of a square pyramid can be calculated using the formula: ( \text{Lateral Area} = 2 \times \text{base length} \times \text{slant height} ). Here, the base length refers to the length of one side of the square base, and the slant height is the height of the triangular face from the base to the apex of the pyramid. To find the total lateral area, simply plug in the values for the base length and slant height into the formula.
What is the height of each lateral face of a pyramid called?
The height of each lateral face of an unspecified object is unknowable.
What happens to the lateral sides of a pyramid when the height of the pyramid is increased and the size of the base is decreased?
The lateral sides get taller and narrower. (:
What is the surface area of a square pyramid?
It is the lateral area (which is 1/2 the perimeter multiplied by the slant height), plus the area of the base.
How do you find the lateral height of a square pyramid?
To find the lateral height of a square pyramid, first identify the apex (top point) of the pyramid and the midpoint of one of its base sides. The lateral height is the length of the segment connecting the apex to this midpoint. You can use the Pythagorean theorem, where the lateral height forms the hypotenuse of a right triangle with the height of the pyramid and half the base length as the two other sides. Thus, the formula is ( l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2} ), where ( l ) is the lateral height, ( h ) is the height, and ( b ) is the length of a base side.
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.
In the equation for the lateral area of a regular pyramid one can replace the slant height with the altitude of the pyramid?
False
