Question

Angelina drew a net of a container in the shape of a triangular pyramid. The base is an isosceles triangle with sides measuring 24 cm, 20 cm, and 20 cm.Which statement about the area of the pyramid is true?

A. The base cm is 384cm
B.The Lateral area is 692cm
C.The surface area is 740cm
D. The area of each congruent face is 264cm

Answer 1

Option B. The Lateral area is 692 cm2

Explanation:

Verify each statement

case A) The area of the base is 384 cm2

The statement is False

Because

The area of the base is

`B=(1)/(2)(24)(16)=192\ cm^(2)`

case B) The Lateral area is 692 cm2

The statement is True

Because

we know that

The lateral area is equal to the area of its three triangular lateral faces

so

`LA=2((1)/(2)(20)(22))+ (1)/(2)(24)(21)=692\ cm^(2)`

case C) The surface area is 740 cm2

The statement is False

we know that

The surface area is equal to the lateral area plus the area of the base

so

`SA=LA+B`

we have

`LA=692\ cm^(2)`

`B=192\ cm^(2)`

substitute

`SA=692+192=884\ cm^(2)`

case D) The area of each congruent face is 264 cm2

The statement is False

The area of each congruent face is equal to

`A=(1)/(2)(20)(22)=220\ cm^(2)`