Question

100 points please HELP asap!!! (05.01)Which statement best describes the area of the triangle shown below?

It is one-half the area of a rectangle of length 4 units and width 2 units.
It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a square of side length 4 units.

Answer 1

Option B:

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

Solution:

Base of the triangle = 4 units

Height of the triangle = 4 units

Area of the triangle =
`(1)/(2) *\text{base}*\text{height}`

`$=(1)/(2)*{4}*{4}`

Area of the triangle = 8 square units

Option A: It is one-half the area of a rectangle of length 4 units and width 2 units.

Area of the rectangle = 4 × 2 = 8 square units

Half of rectangle =
`(1)/(2)*8=4` square units

It is not true because area of the triangle is 8 square units.

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

Area of the square = 4 × 4 = 16 square units

Half of square =
`(1)/(2)*16=8` square units

It is true because area of the triangle is 8 square units.

Option C: It is twice the area of a rectangle of length 4 units and width 2 units.

Area of the rectangle = 4 × 2 = 8 square units

Twice of rectangle = 2 × 8 = 16 square units

It is not true because area of the triangle is 8 square units.

Option D: It is twice the area of a square of side length 4 units.

Area of the square = 4 × 4 = 16 square units

Twice of square = 2 × 16 = 32 square units

It is not true because area of the triangle is 8 square units.

Hence Option B is the correct answer.

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