Respuesta :
The 3rd statement is true.
The area of a triangle is 1/2 the area of a rectangle with the same base and height.
The area of a triangle is 1/2 the area of a rectangle with the same base and height.
Answer:
It is one-half the area of a rectangle of length 4 units and width 3 units.
Step-by-step explanation:
Base of triangle = 4 units.
Height of triangle = 3 units
Formula of area of triangle : [tex]\frac{1}{2} \times Base \times Height[/tex]
So, the area of the given triangle = [tex]\frac{1}{2} \times4 \times 3[/tex]
= [tex]\frac{12}{2}[/tex]
= [tex]6units^2[/tex]
Option 1: It is twice the area of a rectangle of length 4 units and width 3 units.
Area of rectangle : [tex]Length \times Width[/tex]
= [tex]4 \times 3[/tex]
=[tex]12 units^2[/tex]
Area of triangle is 6 square units
Area of rectangle is 12 square units
[tex]6\neq2\times12[/tex]
[tex]6\neq24[/tex]
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 = [tex](side)^2[/tex]
= [tex](3)^2[/tex]
=[tex]9[/tex]
Area of triangle is 6 square units.
Area of square is 9 square units .
[tex]6\neq2\times9[/tex]
[tex]6\neq18[/tex]
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 : [tex]Length \times Width[/tex]
= [tex]4 \times 3[/tex]
=[tex]12 units^2[/tex]
Area of triangle is 6 square units
Area of rectangle is 12 square units
[tex]6=\frac{1}{2}\times12[/tex]
[tex]6=6[/tex]
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 = [tex](side)^2[/tex]
= [tex](3)^2[/tex]
=[tex]9[/tex]
Area of triangle is 6 square units.
Area of square is 9 square units .
[tex]6\neq \frac{1}{2} \times 9[/tex]
[tex]6\neq 4.5[/tex]
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.
