What's the lateral area of the following pyramid? : 129.6 cm² 172.8 cm² 86.4 cm² 259.2 cm²

129.6 cm²

Step-by-step explanation:

The lateral area (A) is the area of the 4 congruent triangular faces.

A = 4 × bh ( b is the base and h the perpendicular height )

Here b = 8 and h = 8.1 , thus

A = 4 × × 8 × 8.1 = 2 × 8 × 8.1 = 16 × 8.1 = 129.6 cm²

Inverse Variation

Inverse Variation

The statement "y varies inversely as x means that when x increases, ydecreases by the same factor. In other words, the expression xy is constant:

xy = k    

where k is the constant of variation.

We can also express the relationship between x and y as:

y =      

where k is the constant of variation.

Since k is constant, we can find k given any point by multiplying the x-coordinate by the y-coordinate. For example, if y varies inversely as x, and x = 5 when y = 2, then the constant of variation is k = xy = 5(2) = 10. Thus, the equation describing this inverse variation is xy = 10 or y = .

Example 1: If y varies inversely as x, and y = 6 when x = , write an equation describing this inverse variation.

k = (6) = 8  

xy = 8 or y =  

Example 2: If y varies inversely as x, and the constant of variation is k = , what is y when x = 10?

xy =  

10y =  

y = × = × =  

k is constant. Thus, given any two points (x1, y1) and (x2, y2) which satisfy the inverse variation, x1y1 = k and x2y2 = k. Consequently, x1y1 = x2y2 for any two points that satisfy the inverse variation.

Example 3: If y varies inversely as x, and y = 10 when x = 6, then what is y when x = 15?

x1y1 = x2y2  

6(10) = 15y  

60 = 15y  

y = 4  

Thus, when x = 6, y = 4.