Let’s solve each triangle one by one.
We are told to:
1. Use Pythagoras’ theorem to find the missing side (if needed).
2. Then use the area formula:
Area = ½ × base × height
Remember: In a right triangle, the two sides that form the right angle are the base and height. The hypotenuse is the longest side — opposite the right angle.
---
Problem 1)
Given: Hypotenuse = 13 mm, one leg = 12 mm → find other leg.
Pythagoras:
a² + b² = c²
Let’s say:
x² + 12² = 13²
x² + 144 = 169
x² = 169 - 144 = 25
x = √25 = 5 mm
Now, area = ½ × base × height = ½ × 12 × 5 = 30 mm²
✔ Area =
30 mm²
---
Problem 2)
Given: Hypotenuse = 5 cm, one leg = 4 cm → find other leg.
x² + 4² = 5²
x² + 16 = 25
x² = 9
x = 3 cm
Area = ½ × 4 × 3 = 6 cm²
✔ Area =
6 cm²
---
Problem 3)
Given: Hypotenuse = 17 m, one leg = 8 m → find other leg.
x² + 8² = 17²
x² + 64 = 289
x² = 225
x = 15 m
Area = ½ × 8 × 15 = 60 m²
✔ Area =
60 m²
---
Problem 4)
Given: Hypotenuse = 10 cm, one leg = 6 cm → find other leg.
x² + 6² = 10²
x² + 36 = 100
x² = 64
x = 8 cm
Area = ½ × 6 × 8 = 24 cm²
✔ Area =
24 cm²
---
Problem 5)
Given: Hypotenuse = 3.7 m, one leg = 3.5 m → find other leg.
x² + 3.5² = 3.7²
Calculate squares:
3.5² = 12.25
3.7² = 13.69
So:
x² = 13.69 - 12.25 = 1.44
x = √1.44 = 1.2 m
Area = ½ × 3.5 × 1.2
First: 3.5 × 1.2 = 4.2
Then: ½ × 4.2 = 2.1 m²
✔ Area =
2.1 m²
---
Problem 6)
Given: Hypotenuse = 5.3 cm, one leg = 2.8 cm → find other leg.
x² + 2.8² = 5.3²
Calculate:
2.8² = 7.84
5.3² = 28.09
x² = 28.09 - 7.84 = 20.25
x = √20.25 = 4.5 cm
Area = ½ × 2.8 × 4.5
First: 2.8 × 4.5
Break it down:
2.8 × 4 = 11.2
2.8 × 0.5 = 1.4
Total = 11.2 + 1.4 = 12.6
Then: ½ × 12.6 = 6.3 cm²
✔ Area =
6.3 cm²
---
Final Answer:
1) 30
2) 6
3) 60
4) 24
5) 2.1
6) 6.3
Parent Tip: Review the logic above to help your child master the concept of right triangle worksheet answer key.
