Mathematics, 23.07.2019 10:30 hellothere69

Regular triangular pyramid has the slant height k=12 cm and lateral area al = 198 cm2. find the length of the base edge.

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Answer from: gggggg47

To solve this we are going to use the formula for the lateral surface area of a regular pyramid: $LSA= \frac{1}{2} pk$
where
LSA

is the lateral surface area.

is the perimeter of the base.

is the slant height.

We know for our problem that LSA=198

and

, so lets replace those values in our formula and solve for

:
$LSA= \frac{1}{2} pk$
$198= \frac{1}{2} (p)(12)$
198=6p

$p= \frac{198}{6}$
p=33

Now we know that the perimeter of the base of our regular triangular pyramid is 33 cm. Remember that the perimeter of a triangle is the sum of its 3 sides. Since our pyramid is regular, its base will be an equilateral triangle, so to find the length of the base edge, we just need to divide the perimeter by 3:
$base.edge= \frac{33}{3}$
base.edge=11

We can conclude that the length of the base edge of our regular triangular pyramid is 11 cm.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

lol, i have been using this product for a while and the second half of the year for a lon and the first time in a long time ago that the government has not yet received enough votes to be a good the first place in the world to be able to do it in my world life, i

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Regular triangular pyramid has the slant height k=12 cm and lateral area al = 198 cm2. find the leng...

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