Question

Calculate the area of this right- angled triangle. Give your answer in cm² and give any decimal answers to 1 d.p. 40 cm 24 cm​

Answer 1

Based on the given information, the area of the right-angled triangle is 384
`cm^2`.

How to calculate the area of a right-angled triangle

To calculate the area of a right-angled triangle, use the formula:

Area = (1/2) * base * height

In this case, the adjacent side (base) is given as 24 cm, and the hypotenuse is given as 40 cm.

To find the height, use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem:

`height^2 + base^2 = hypotenuse^2`

`height^2 + 24^2 = 40^2`

`height^2 + 576 = 1600\\height^2 = 1600 - 576\\height^2 = 1024\\height = \sqrt(1024)`

height = 32 cm

Now, calculate the area using the formula:

Area = (1/2) * base * height

Area = (1/2) * 24 cm * 32 cm

Area = 384
`cm^2`

Therefore, the area of the right-angled triangle is 384
`cm^2`.