No
The base and height of a square are always equal to each other. ALWAYS.
The volume of anything is always the area of the base of the object times the height. Therefore, to find the volume the object must have a height, which makes volume work with all 3D shapes. If one is looking at a 2D shape, then there is no height so a volume cannot be calculated (note: areas may be found of 2D shapes).
base: 52 ft
You use base times height to calculate the area of a rectangle or parallelogram when you need to find the space within those shapes. The base refers to one side of the shape, while the height is the perpendicular distance from that side to the opposite side. This formula is applicable when you have a clear base and height measurement, ensuring that they are perpendicular to each other. For other shapes, different formulas may be required.
Yes, the slant height of a regular square pyramid is longer than its altitude. The altitude is the perpendicular height from the apex to the center of the base, while the slant height is the distance from the apex to the midpoint of a side of the base. In a right triangle formed by the altitude, half the base side, and the slant height, the slant height serves as the hypotenuse, making it inherently longer than the altitude.
Prism M and pyramid N having the same base area and height means they share the same volume formula, where volume for both shapes can be calculated based on these dimensions. Cylinder P and prism Q, with the same height and base perimeter, will have different volumes unless their base shapes are identical. Cone Z having the same base area as cylinder P indicates that while they share the same base, their volumes will differ due to their differing heights and shapes. Overall, the relationships between these shapes depend on their respective dimensions and properties.
the height of a triangle is three feet longer than the base. The area of the triangle is 35 square feet. Find the height andbase of the triangle
There is no relationship, in the sense that you can have any base are with any height. For a prism shape (if the horizontal cross section is always the same as the base), the base area times the height is equal to the volume.
The area formulas for triangles, parallelograms, and trapezoids are derived from the area of a rectangle, as they can be thought of as derived shapes. The area of a rectangle is calculated as base times height (A = base × height). For a triangle, the area is half that of a rectangle with the same base and height (A = 1/2 × base × height). A parallelogram retains the rectangle's base and height relationship (A = base × height), while a trapezoid can be viewed as a rectangle with two triangles removed or added, leading to its area formula (A = 1/2 × (base1 + base2) × height).
Because it is the base times the height.
The area of a parallelogram is base x height and the area of a triangle is 1/2 x base x height. So the area of a parallelogram will always be 2 times bigger than a triangle with the same base and height.
To find the area of a triangle, the base is used, along with the corresponding height. For a parallelogram, either pair of opposite sides can serve as the base, with the height being the perpendicular distance from that base to the opposite side. The area calculations for both shapes involve multiplying the base by the height and dividing by two for the triangle.