Question

1.What is the area, in square units, of the parallelogram shown below?

12 square units
18 square units
24 square units
36 square units
2.Which statement best describes the area of Triangle ABC shown below?



It is one-half the area of a rectangle with sides 2 units × 3 units.
It is twice the area of a rectangle with sides 2 units × 3 units.
It is one-half the area of a square of side length 3 units.
It is twice the area of a square of side length 3 units

Answer 1

1) 24 square units 2) It is one-half the area of a rectangle with sides 2 units × 3 units.

Explanation:

`Area_(Parallelogram)=width*length\\A=6*4\\A=24 u^(2)`

The area of a parallelogram is calculated by width times height, height is always a perpendicular segment.

2)Which statement best describes the area of Triangle ABC shown below?

Counting the squares, we can see there is a 2 squares for the base and 3 for the height.

`\bigtriangleup ABC=(b*h)/(2)\\ \bigtriangleup ABC=(2*3)/(2)=3`

The Area of a Rectangle is 6, for S Rect. =2*3=6 One rectangle comprises two triangles.

Answer 2

(C) and (A)

Explanation:

(A) It is given that ABCD is a parallelogram with base DC=4 units and height is 6 units, thus the area of parallelogram is given as:

`A=Base{*}height`

Substituting the given values, we have

`A=4{*}6`

`A=24 sq units`

Therefore, the area of the parallelogram is 24 square units.

Hence, Option (C) is correct.

(B) We are given a triangle which is inside the rectangle with sides 2 units × 3 units, therefore the area of the triangle ABC will be:

`Area=(1)/(2)(area of rectangle)`

Thus, the area of triangle ABC will be one-half the area of a rectangle with sides 2 units × 3 units.

Hence, option A is correct.