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The area of the triangle ABC is 2.24 sq. meter.

The length of AC is 3.2 m

Step-by-step explanation:

(a) To find the area of the triangle ABC :

The formula for area of triangle = 1/2 × base × height

⇒ 1/2 × 1.6 × 2.8

⇒ 4.48/2

⇒ 2.24 square meter.

Therefore, the area of the triangle ABC is 2.24 sq. meter.

(b) To calculate the length of AC :

Use the Pythagorean theorem to find the third side(hypotenuse) of a right triangle,

⇒ AC² = AB² + BC²

It is given that, the length of AB is 1.6 and the length of BC is 2.8

⇒ AC² = (1.6)² + (2.8)²

⇒ AC² = 2.56 + 7.84

⇒ AC² = 10.4

Taking square root on both sides,

⇒ AC = √10.4

⇒ AC = 3.2

Therefore, the length of AC is 3.2 m