Answer:
74.72 units.
Step-by-step explanation:
To find the perimeter of the figure, we need to determine the lengths of all its sides. The figure consists of a right-angled trapezoid
ABCE, where
AB and
EC are perpendicular to
BC and
AE is inclined at an angle of 70°.
Given:
=
8
AB=8
=
10
BC=10
∠
=
70
°
∠AEC=70°
We need to find the lengths of
AE and
EC.
Step 1: Calculate the length of
EC
Since
AB is perpendicular to
BC, the angle between
BC and
EC is also 90°. Thus, we can use trigonometry in the right triangle
AEC.
Using the sine function:
sin
(
70
°
)
=
sin(70°)=
AE
EC
Step 2: Calculate the length of
AE
Using the cosine function:
cos
(
70
°
)
=
cos(70°)=
AE
BC
=
cos
(
70
°
)
AE=
cos(70°)
BC
=
10
cos
(
70
°
)
AE=
cos(70°)
10
Using the value
cos
(
70
°
)
≈
0.3420
cos(70°)≈0.3420:
=
10
0.3420
≈
29.24
AE=
0.3420
10
≈29.24
Step 3: Calculate the length of
EC
Using the sine function:
=
⋅
sin
(
70
°
)
EC=AE⋅sin(70°)
=
29.24
⋅
sin
(
70
°
)
EC=29.24⋅sin(70°)
Using the value
sin
(
70
°
)
≈
0.9397
sin(70°)≈0.9397:
=
29.24
⋅
0.9397
≈
27.48
EC=29.24⋅0.9397≈27.48
Step 4: Calculate the perimeter
Now we have the lengths of all sides:
=
8
AB=8
=
10
BC=10
=
29.24
AE=29.24
=
27.48
EC=27.48
The perimeter
P of the figure is the sum of the lengths of all sides:
=
+
+
+
P=AB+BC+AE+EC
=
8
+
10
+
29.24
+
27.48
≈
74.72
P=8+10+29.24+27.48≈74.72
Therefore, the perimeter of the figure is approximately
74.72
74.72 units.
