The surface area of the triangular prism pictured below is 204 square centimeters. What is the height of the prism?
1 answer:
The picture in the attached figure
we know that
surface area=2*area of the base+perimeter*height
area of the base=area of the triangle
area of the base=3*4/2----> 6 cm²
perimeter of the base=perimeter of triangle
perimeter=3+4+5----> 12 cm
height=x cm
surface area=2*6+12*x
surface area=204 cm²
12+12*x=204
12*x=204-12
12*x=192
x=192/12
x=16 cm
the answer is
16 cm
we know that
surface area=2*area of the base+perimeter*height
area of the base=area of the triangle
area of the base=3*4/2----> 6 cm²
perimeter of the base=perimeter of triangle
perimeter=3+4+5----> 12 cm
height=x cm
surface area=2*6+12*x
surface area=204 cm²
12+12*x=204
12*x=204-12
12*x=192
x=192/12
x=16 cm
the answer is
16 cm
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Reason 3: Definition of Parallelogram
Reason 4: Alternate Interior Angles Theorem
Reason 5: Reflexive Property of Congruence
Reason 6: ASA Congruence Property
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Explanations:
Explanation for Reason 3: A parallelogram, by definition, has opposite sides that are parallel. It's built into the name more or less. Sides AB and CD are opposite one another in the parallelogram so they are parallel segments
Explanation for Reason 4: Angle ABD is congruent to angle CDB because they are alternate interior angles. They are on the inside of the "train tracks" that are formed by AB and CD. They lay on opposite sides of the transversal BD
Explanation for Reason 5: Any segment is congruent to itself; ie, the same length
Explanation for Reason 6: Using reasons 2,5 and 4, we can use ASA (angle side angle) to prove the two triangles ABD and CDB congruent. Reason 2 is the first "A" in ASA. Reason 5 is the S in ASA. Reason 4 is the other A in ASA. The side is between the two pairs of angles. See the attache image for a visual summary of how ASA is being used.
Reason 3: Definition of Parallelogram
Reason 4: Alternate Interior Angles Theorem
Reason 5: Reflexive Property of Congruence
Reason 6: ASA Congruence Property
------------------------------------------------------
Explanations:
Explanation for Reason 3: A parallelogram, by definition, has opposite sides that are parallel. It's built into the name more or less. Sides AB and CD are opposite one another in the parallelogram so they are parallel segments
Explanation for Reason 4: Angle ABD is congruent to angle CDB because they are alternate interior angles. They are on the inside of the "train tracks" that are formed by AB and CD. They lay on opposite sides of the transversal BD
Explanation for Reason 5: Any segment is congruent to itself; ie, the same length
Explanation for Reason 6: Using reasons 2,5 and 4, we can use ASA (angle side angle) to prove the two triangles ABD and CDB congruent. Reason 2 is the first "A" in ASA. Reason 5 is the S in ASA. Reason 4 is the other A in ASA. The side is between the two pairs of angles. See the attache image for a visual summary of how ASA is being used.
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Step-by-step explanation:
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