Question

Use Pythagoras to find the height and hence, the area of the triangle

below. Give height to 1 decimal place and area to the nearest whole. Write
answer in format: h= A= *
20 mm
Val

Answer 1

h=17.3 A=173

Explanation:

Calculator

Answer 2

height = 17.3 mm

area = 173 mm²

Explanation:

all three sides are of the same length (20 mm).

so, the height actually splits the baseline in half

(2 × 10 mm) while hitting it at a 90 degree angle.

so, we use Pythagoras, where the full side opposite of this 90 degree angle is c (Hypotenuse), the height of the main triangle is one side, and half of the baseline is the other side.

c² = a² + b²

20² = 10² + height²

400 = 100 + height²

300 = height²

height = 17.3 mm

the area of the main triangle is baseline (20) times height divided by 2.

so,

At = 20×17.3/2 = 10×17.3 = 173 mm²