Question

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

Answer 1

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

Answer 2

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

Find the hypotenuse of the triangle

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

Find the perimeter of triangle

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

Find the lateral area

$LA=Ph$

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

Find the area of the base B

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

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