nalyzing Intersections of Lines and Planes The left vertical plane intersects the horizontal plane at line x. The right vertical
2 answers:
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Answer:
Part A) The area of triangle i is
Part B) The total area of triangles i and ii is
Part C) The area of rectangle i is
Part D) The area of rectangle ii is
Part E) The total area of rectangles i and iii is
Part F) The total area of all the rectangles is
Part G) To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i
Part H) The surface area of the prism is
Part I) The statement is false
Part J) The statement is true
Step-by-step explanation:
Part A) What is the area of triangle i?
we know that
The area of a triangle is equal to
we have
substitute
Part B) Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii?
we know that
If Triangles i and ii are congruent
then
Their areas are equal
so
The area of triangle ii is equal to
The total area of triangles i and ii is equal to
substitute the values
Part C) What is the area of rectangle i?
we know that
The area of a rectangle is equal to
we have
substitute
Part D) What is the area of rectangle ii?
we know that
The area of a rectangle is equal to
we have
substitute
Part E) Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii?
we know that
Rectangles i and iii are congruent (have the same size and shape)
If rectangles i and iii are congruent
then
Their areas are equal
so
The area of rectangle iii is equal to
The total area of rectangles i and iii is equal to
substitute the values
Part F) What is the total area of all the rectangles?
we know that
The total area of all the rectangles is
substitute the values
Part G) What areas do you need to know to find the surface area of the prism?
To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i
Part H) What is the surface area of the prism? Show your calculation
we know that
The surface area of the prism is equal to the area of all the faces of the prism
so
The surface area of the prism is two times the area of triangle i plus two times the area of rectangle i plus the area of rectangle ii
Part I) Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?
The statement is false
Because, the three rectangles are not congruent
The total area of the rectangles is and if you multiply the area of one rectangle by 3 you will get
Part J) Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?
The statement is true
Because, the triangles are congruent
Answer: c= -4.7
Step-by-step explanation:
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