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yaroslaw [1]
3 years ago
5

Find the lateral area for the prism. L.A. = Find the total area for the prism. T.A. =

Mathematics
2 answers:
Ksivusya [100]3 years ago
6 0
The lateral area of the prism is given by:
LA=[area of the two triangles]+[area of the lateral rectangles]
hypotenuse of the triangle will be given by Pythagorean:
c^2=a^2+b^2
c^2=6^2+4^2
c^2=52
c=sqrt52
c=7.211'
thus the lateral area will be:
L.A=2[1/2*4*6]+[6*8]+[8*7.211]
L.A=24+48+57.69
L.A=129.69 in^2

The total are will be given by:
T.A=L.A+base area
base area=length*width
=4*8
=32 in^2
thus;
T.A=32+129.69
T.A=161.69 in^2

mote1985 [20]3 years ago
6 0

Answer:

Part 1) LA=(80+16\sqrt{13})\ in^{2}

Part 2) TA=(104+16\sqrt{13})\ in^{2}

Step-by-step explanation:

Part 1) Find the lateral area of the prism

we know that

The lateral area of the prism is equal to

LA=Ph

where

P is the perimeter of the base

h is the height of the prism

Applying the Pythagoras Theorem

<u>Find the hypotenuse of the triangle</u>

c^{2}=4^{2}+6^{2}\\ \\c^{2}=52\\ \\c=2\sqrt{13}\ in

<u>Find the perimeter of triangle</u>

P=4+6+2\sqrt{13}=(10+2\sqrt{13})\ in

<u>Find the lateral area</u>

LA=Ph

we have

P=(10+2\sqrt{13})\ in

h=8\ in

substitutes

LA=(10+2\sqrt{13})*8=(80+16\sqrt{13})\ in^{2}

Part 2) Find the total area of the prism

we know that

The total area of the prism is equal to

TA=LA+2B

where

LA is the lateral area of the prism

B is the area of the base of the prism

<u>Find the area of the base B</u>

The area of the base is equal to the area of the triangle

B=\frac{1}{2}bh

substitute

B=\frac{1}{2}(6)(4)=12\ in^{2}

Find the total area of the prism

TA=LA+2B

we have

B=12\ in^{2}

LA=(80+16\sqrt{13})\ in^{2}

substitute

TA=(80+16\sqrt{13})+2(12)=(104+16\sqrt{13})\ in^{2}




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