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kolbaska11 [484]

3 years ago

5

A rectangular pyramid has a height of 10 meters. The base measures 8 meters in length and 12 meters in width. Two different tria

ngular cross sections are formed through the vertex and perpendicular to the base. What is the difference in the areas of the cross sections?

1 answer:

trasher [3.6K]3 years ago

4 0

Step 1
find the a<span>rea of the first cross section

area1=b1*h/2
b1=8 m
h=10 m
area1=6*10/2------> 30 m</span>²

step 2
find the area of the second cross section

area 2=b2*h/2
b2=12 m
h=10 m
area1=12*10/2------> 60 m²

step 3
find <span>the difference in the areas of the cross sections
</span>difference=60-30------> 30 m²

the answer is
30 m²

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Step-by-step explanation:

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Let the vertices be represented with A,B,C,D such as

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To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

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Here, we consider A = (0,1); B = (3,4);

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Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}$

$AB = \sqrt{( - 3)^2 + (-3)^2}$

$AB = \sqrt{9+ 9}$

$AB = \sqrt{18}$

$AB = \sqrt{9*2}$

$AB = \sqrt{9}*\sqrt{2}$

$AB = 3\sqrt{2}$

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

$(x_1,y_1) = B (3,4)$

$(x_2,y_2) = C(4,3)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}$

$BC = \sqrt{(-1)^2 + (1)^2}$

$BC = \sqrt{1 + 1}$

$BC = \sqrt{2}$

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = C(4,3)$

$(x_2,y_2) = D (3,0)$

Substitute these values in the formula above

$Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}$

$CD = \sqrt{(1)^2 + (3)^2}$

$CD = \sqrt{1 + 9}$

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Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

$(x_1,y_1) = D (3,0)$

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Substitute these values in the formula above

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Divide both sides by $\sqrt{10}$

$b = 2$

Hence,

a + b = 2 + 10

a + b = 12

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2 years ago

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To convert the point intercept form to the standard form, we do as follows:

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6 0

1 year ago