If the length of each of the two equal sides of an isosceles triangle is 15 cm and the adjacent angle is 30°, then the area of the triangle is:
- A66.25 cm²
- B36.25 cm²
- C56.25 cm²
- D26.25 cm²
Solution & Step-by-step Explanation
The area of a triangle when two adjacent sides a and b and the included angle θ are given is computed using the formula:
Area=
2
1
absinθ
For the given isosceles triangle:
Side a=15cm
Side b=15cm
Angle θ=30
∘
Substituting the values into the formula:
Area=
2
1
×15×15×sin(30
∘
)
Since sin(30
∘
)=
2
1
:
Area=
2
1
×225×
2
1
=
4
225
=56.25cm
2
Area=
2
1
absinθ
For the given isosceles triangle:
Side a=15cm
Side b=15cm
Angle θ=30
∘
Substituting the values into the formula:
Area=
2
1
×15×15×sin(30
∘
)
Since sin(30
∘
)=
2
1
:
Area=
2
1
×225×
2
1
=
4
225
=56.25cm
2