Triangle ABC is right-angled at A. If AB = 7 cm and AC = 22 cm, determine its area.

The correct answer is 77 cm².

Step 1: Understand the given properties of the triangle
We are given a triangle ABC which is right-angled at vertex A.
In a right-angled triangle, the two perpendicular sides forming the 90° angle serve as the base and the height (altitude).
Since the right angle is at A, the two perpendicular sides are AB and AC:
• Base (AB) = 7 cm
• Height (AC) = 22 cm

Step 2: Recall the formula for the area of a right triangle
The area of a right-angled triangle is given by half the product of its base and height:

$\text{Area}=\frac{1}{2}\times \text{Base}\times \text{Height}$

Step 3: Substitute the values and calculate the area
Substitute the base value of 7 cm and height value of 22 cm into the formula:

$\text{Area}=\frac{1}{2}\times 7\times 22$

Simplify by dividing 22 by 2:

$\text{Area}=7\times 11$

$\text{Area}=77{\text{cm}}^2$

Thus, the area of triangle ABC is equal to 77 cm².