FIND THE LATERAL AREA OF A RIGHT PYRAMID WHOSE SLANT HEIGHT IS 18mm AND WHOSE BASE IS A SQUARE WITH AN AREA 121mm^2
The length of the base (b) of each triangular side is sqrt 121 = 11 mm. The height (h) of each triangle is the 18 mm slant height. Therefore each of the four sides has an area of
1/2 (base)*(height) = 11*18/2 = 99 mm^2
The total lateral area is therefore 4*99 = 396 mm^2
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To find the lateral area of a right pyramid, you need to know the slant height and the base area.
In this case, the slant height is given as 18mm and the base area is given as 121mm^2.
Step 1: Find the perimeter of the base square.
Since the base is a square, all four sides are equal in length. To find the perimeter of the base, you can simply multiply one side length by 4.
Let's call the side length of the base square "s".
s = √(area of base square) = √121mm^2 = 11mm
Perimeter of the base square = 4s = 4 * 11mm = 44mm
Step 2: Find the lateral area of the pyramid.
The lateral area of the pyramid is the sum of the areas of the four triangular faces.
To find the area of each triangular face, we can use the formula: Area = 0.5 * base * height.
In this case, the base is the side length of the base square (11mm), and the height is the slant height of the pyramid (18mm).
Area of one triangular face = 0.5 * 11mm * 18mm = 99mm^2
Since there are four triangular faces in a right pyramid, the total lateral area can be calculated by multiplying the area of one triangular face by 4.
Total lateral area = 4 * 99mm^2 = 396mm^2
Therefore, the lateral area of the given right pyramid is 396mm^2.
To find the lateral area of a right pyramid, you need to know the slant height and the area of the base.
Let's start by calculating the length of one side of the square base. Since the area of the square base is given as 121 mm^2, we can find the length of one side by taking the square root of the area.
Side length of the square = √(Area of the square base) = √121 mm = 11 mm
Now, we know the slant height and the side length of the square base. To find the lateral area, we need to calculate the perimeter of the base, and then multiply it by half the slant height.
Perimeter of the base = 4 × Side length of the square = 4 × 11 mm = 44 mm
Lateral area of the pyramid = (Perimeter of the base) × (Slant height / 2)
= 44 mm × (18 mm / 2)
= 44 mm × 9 mm
= 396 mm^2
Therefore, the lateral area of the right pyramid is 396 mm^2.