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(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.

User Amy Doxy
by
6.7k points

2 Answers

3 votes

Answer:

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.

User Ilam Engl
by
6.5k points
3 votes
The 3rd statement is true.

The area of a triangle is 1/2 the area of a rectangle with the same base and height.
User Sameer Manek
by
7.3k points