Question

(05.01)Which statement best describes the area of the triangle shown below?

A coordinate grid is shown with a triangle. The base is 4 units, and the height is 3 units.

It is twice the area of a rectangle of length 4 units and width 3 units.
It is twice the area of a square of side length 3 units.
It is one-half the area of a rectangle of length 4 units and width 3 units.
It is one-half the area of a square of side length 3 units.

Answer 1

It is one-half the area of a rectangle of length 4 units and width 3 units.

Explanation:

Base of triangle = 4 units.

Height of triangle = 3 units

Formula of area of triangle :
`(1)/(2) * Base * Height`

So, the area of the given triangle =
`(1)/(2) *4 * 3`

=
`(12)/(2)`

=
`6units^2`

Option 1: It is twice the area of a rectangle of length 4 units and width 3 units.

Area of rectangle :
`Length * Width`

=
`4 * 3`

=
`12 units^2`

Area of triangle is 6 square units

Area of rectangle is 12 square units

`6\\eq2*12`

`6\\eq24`

So, area of triangle is half the area of rectangle of length 4 units and width 3 units. .

Hence Option 1 is wrong .

Option 2: It is twice the area of a square of side length 3 units.

Area of square =
`(side)^2`

=
`(3)^2`

=
`9`

Area of triangle is 6 square units.

Area of square is 9 square units .

`6\\eq2*9`

`6\\eq18`

So, area of triangle is not twice the area the area of a square of side length 3 units.

Hence Option 2 is wrong .

Option 3: It is one-half the area of a rectangle of length 4 units and width 3 units.

Area of rectangle :
`Length * Width`

=
`4 * 3`

=
`12 units^2`

Area of triangle is 6 square units

Area of rectangle is 12 square units

`6=(1)/(2)*12`

`6=6`

So, area of triangle is half the area of rectangle of length 4 units and width 3 units.

Hence Option 3 is right.

Option 4 : It is one-half the area of a square of side length 3 units.

Area of square =
`(side)^2`

=
`(3)^2`

=
`9`

Area of triangle is 6 square units.

Area of square is 9 square units .

`6\\eq (1)/(2) * 9`

`6\\eq 4.5`

Hence Option 4 is wrong .

Hence Option 3 is correct :It is one-half the area of a rectangle of length 4 units and width 3 units.

Answer 2

The 3rd statement is true.

The area of a triangle is 1/2 the area of a rectangle with the same base and height.