Mathematics: line A passes through the points (4,9) and.(12,23). line b passes through the points (0,2) and (-8,-12) which statement is true

line A passes through the points (4,9) and.(12,23).

Ответ:

flore7488

30.10.2020

Mathematics

The total surface area of the prism is $SA=288\ in^{2}$

Step-by-step explanation:

we know that

The two diagonals of a rhombus are perpendicular and bisect each other

All sides are congruent

The surface area of a prism is equal to

SA=2B+Ph

where

B is the area of the base of prism

P is the perimeter of the base of prism

h is the height of the prism

step 1

Find the length side of the rhombus

Applying Pythagoras Theorem

$c^{2}=a^{2}+b^{2}$

we have

c is the length side of the rhombus

a and b are the semi diagonals of the rhombus

$a=8/2=4\ in$

$b=6/2=3\ in$

substitute

$c^{2}=4^{2}+3^{2}$

$c^{2}=25$

$c=5\ in$

step 2

Find the perimeter of the base P

The perimeter of the rhombus is equal to

P=4c

$P=4(5)=20\ in$

step 3

Find the area of the base B

The area of the rhombus is

$B=\frac{1}{2}[D1*D2]$

D1 and D2 are the diagonals of the rhombus

substitute

$B=\frac{1}{2}[8*6]=24\ in^{2}$

step 3

Find the surface area of the prism

SA=2B+Ph

substitute the values

SA=2(24)+(20)(12)

$SA=288\ in^{2}$

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line A passes through the points (4,9) and.(12,23). line b passes through the points (0,2) and (-8,-12) which statement is true

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