Question

Which statements are true about the rectangular pyramid below? Select three options.

A rectangular pyramid. The rectangular base has a length of 6 centimeters and width of 4 centimeters. 2 triangular sides have a base of 6 centimeters and height of 6 centimeters. 2 triangular sides have a base of 4 centimeters and height of 4.6 centimeters.
The area of the base is 24 cm2.
There are four lateral faces.
All the lateral faces are congruent.
The total surface area of the figure is 66.4 cm2.
At least one of the lateral faces has an area equal to 24 cm2.

Answer 1

Answer:

The area of the base is 24 cm2.

There are four lateral faces

Step-by-step explanation:

Verify each statement

case 1) The area of the base is 24 cm2.

The statement is true

Because the base is a rectangle

The area of rectangle is

$B=LW$

substitute the given values

$B=(6)(4)=24\ cm^2$

case 2) There are four lateral faces

The statement is true

Because a rectangular pyramid has a rectangular base and four triangular lateral faces

case 3) All the lateral faces are congruent

The statement is false

Because only two lateral faces are congruent with the other two lateral faces

case 4) The total surface area of the figure is 66.4 cm2.

The statement is false

Because, the surface area is equal to the area of a rectangle plus the area of four triangles

so

$SA=(6)(4)+2[\frac{1}{2}(6)(6)]+2[\frac{1}{2}(4)(4.6)]$

$SA=24+36+18.4=78.4\ cm^2$

case 5) At least one of the lateral faces has an area equal to 24 cm2

The statement is false

The base of the pyramid has an area equal to 24 square centimeters but none of the lateral triangular sides have an area equal to 24 square centimeters

Answer 2

Answer:

1, 2, 4

Step-by-step explanation:

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