Mathematics: Apackage is in the shape of a triangular prism. the bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. the distance between the bases is 10 centimeters. what is the surface area of the triangular prism? 210 square centimeters 318 square centimeters 360 square centimeters 468 square centimeters

Apackage is in the shape of a triangular prism.

Ответ:

lexylexy8583

13.03.2022

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.

Step-by-step explanation:

It is given that the bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. Using Pythagoras theorem, the third side of the base is

hypotenuse^2=leg_1^2+leg_2^2

hypotenuse^2=(9)^2+(12)^2

hypotenuse^2=225

$hypotenuse=\sqrt{225}$

hypotenuse=15

The area of a triangle is

$A=\frac{1}{2}\times base \times height$

Area of the base is

$A_1=\frac{1}{2}\times 9\times 12=54$

The curved surface area of triangular prism is

$A_2=\text{perimeter of base}\times height$

$A_2=(9+12+15)\times 10$

$A_2=9\times 10+12\times 10+15\times 10$

A_2=360

The surface area of the triangular prism is

A=2A_1+A_2

A=2(54)+360

A=108+360

A=468

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.

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Ответ:

Fredo10

04.11.2021

Mathematics

a. ∫ xSinx dx

iii. integration by parts

u =x and dv= sinx

b. ∫ x⁴/(1+x³). dx

ii. neither

Long division is an option here before integration is done

c. ∫ x⁴. e^x³. dx

i. substitution

where u = x⁵

d. ∫x⁴ cos(x⁵). dx

i. substitution

where u = x⁵

e. ∫1/√9x+1 .dx

i. substitution

where u = 9x+1

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