Question

Area and the pythagorean theorem.

Answer 1

Explanation:

the area of a triangle is

baseline × height / 2

in case of a right-angled triangle we can use the legs (they are standing in 90° to each other) as baseline and height.

we need Pythagoras to find the length of the second leg.

a² + b² = c²

with c being the Hypotenuse, and a and b are the legs.

so,

26² = 10² + leg2²

676 = 100 + leg2²

576 = leg2²

leg2 = 24 cm

so, the area of the triangle is

10 × 24 / 2 = 10×12 = 120 cm²

remember, an area is always expressed in square units. a length in basic units, and a volume in cubic units.

Answer 2

A = 120 cm²

Explanation:

the area (A) of a triangle is calculated as

A =
`(1)/(2)` bh ( b is the base and h the perpendicular height )

here b = 10 , we require to calculate h

using Pythagoras' identity in the right triangle

h² + 10² = 26²

h² + 100 = 676 ( subtract 100 from both sides )

h² = 576 ( take square root of both sides )

h =
`√(576)` = 24

Then

A =
`(1)/(2)` × 10 × 24 = 5 × 24 = 120 cm²