Answer:
Perimeter = 18.7 units
Area = 13.5 units²
Step-by-step explanation:
Perimeter of ADEC = AD + DE + EC + AC
Length of AD = 3 units
By applying Pythagoras theorem in ΔDBE,
DE² = DB² + BE²
DE² = 3² + 3²
DE = √18
DE = 4.24 units
Length of EC = 3 units
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
AC² = 6² + 6²
AC = √72
AC = 8.49 units
Perimeter of ADEC = 3 + 4.24 + 3 + 8.49
= 18.73 units
≈ 18.7 units
Area of ADEC = Area of ΔABC - Area of ΔBDE
Area of ΔABC =
=
= 18 units²
Area of ΔBDE =
=
= 4.5 units²
Area of ADEC = 18 - 4.5
= 13.5 units²
Answer:
x = 25°
Step-by-step explanation:
3x + 2x + x + 30° = 180°
6x + 30° = 180°
6x = 150°
x =25°
=> 3x = 25 * 3 = 75°
=> 2x = 25 * 2 = 50°
=> x + 30° = 25° + 30° = 55°
The figure consists of three objects, a rectangle, a trapezoid, a triangle
Find the area of the rectangle
The rectangle is 16 in long and 9 in wide
a₁ = l × w
a₁ = 16 × 9
a₁ = 144 in²
Find the area of the trapezoid
The base of trapezoid is 31 in and 16 in, and the height is 35 - 20 = 15 in.
a₂ = 1/2 × (a + b) × h
a₂ = 1/2 × (31 + 16) × 15
a₂ = 1/2 × 47 × 15
a₂ = 352.5 in²
Find the area of the triangle
The base of the triangle is 31 in, the height is 20 in
a₃ = 1/2 × b × h
a₃ = 1/2 × 31 × 20
a₃ = 310 in²
Add the area together
a = a₁ + a₂ + a₃
a = 144 + 352.5 + 310
a = 806.5
The answer is 806.5 in²