Question

What is the area of this parallelogram? 10.35 cm² 12.5 cm² 20.25 cm² 30.6 cm² Parallelogram A B C D is composed of a square and two triangles. The square has a length and height of 4.5 centimeters each. There are two identical triangles. Each triangle has a base of 2.3 centimeters and a height of 4.5 centimeters.

Answer 1

30.6 cm²

Explanation:

Dividing the parallelogram into 2 geometry shapes:

Square

2 Right angle triangles

Area of a square, As = length^2

= 4.5^2

= 20.25 cm^2

Area of a right angle triangle, At = 1/2 × base × height

= 1/2 × 2.3 × 4.5

= 5.175 cm^2

Sinve there are 2 right angle triangle,

At = 2 × 5.175

= 10.35 cm^2

Total area of the parallelogram, Ap = area of the square + area of the 2 right angle triangle

= 10.35 + 20.25

= 30.6 cm^2

Answer 2

30.6 cm²

Explanation:

The area of the parallelogram is simply the sum of the areas of the component three shapes - the square and the two triangles.

Area of square = 4.5 cm × 4.5 cm = 20.25 cm²

Area of two triangles = 2 ×(1/2) × 2.3 cm × 4.5 cm = 10.35 cm²

Area of parallelogram = 20.25 cm² + 10.35 cm² = 30.6 cm²