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# What is the area of the two-dimensional cross section that is parallel to face ABC ?

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What is the area of the two-dimensional cross section that is parallel to face ABC ?

? ft² Jun 4, 2019
edited by jiminblossoms  Jun 4, 2019

#1
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The two-dimensional cross-section that is parallel to face ABC is just the triangle ABC.

We need to find the area of ABC.

Since it is a right triangle, we can use the Pythagorean theorem.

5^2+x^2=13^2

25+x^2=169

x^2=144

x=12

Therefore, the area of ABC is 5*12/2=30 ft^2.

You are very welcome!

:P

Jun 4, 2019

#1
-1

The two-dimensional cross-section that is parallel to face ABC is just the triangle ABC.

We need to find the area of ABC.

Since it is a right triangle, we can use the Pythagorean theorem.

5^2+x^2=13^2

25+x^2=169

x^2=144

x=12

Therefore, the area of ABC is 5*12/2=30 ft^2.

You are very welcome!

:P

CoolStuffYT Jun 4, 2019
#2
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The area of the two-dimensional cross section that is parallel to face ABC.that is Area of Δ DEF = 84 ft²

Step-by-step explanation:

Given : A triangular prism with some side measurement.

We have  to find the area of the two-dimensional cross section that is parallel to face ABC.

Since, the cross section that is parallel to face ABC.

Since, face parallel to ABC is DEF .

And DEF is a triangle with ∠ E = 90°

So, Area of right angled triangle is 1/2 times base times height.

Base = 24 ft

and height is 7 ft

So, Area of Δ DEF = 1/2 times 24 times 7

Simplify , we have,

Area of Δ DEF = 84 ft²

Thus, The area of the two-dimensional cross section that is parallel to face ABC.that is Area of Δ DEF = 84 ft²