Answer:
397.7 m²
Step-by-step Explanation:
Step 1: find m < W
W = 180 - (33+113) (sum of ∆)
W = 34°
Step 2: find side UV using the law of sines


Multiply both sides by sin(34)


(approximated)
Step 3: find the area using the formula, ½*UV*VW*sin(V)
area = ½*29.8*29*sin(113)
Area = 397.7 m² (rounded to the nearest tenth.
Answer:
2x - 13
Step-by-step explanation:
Step 1 :
1
Simplify —
2
Equation at the end of step 1 :
1
(-4x - 2) + (— • (12x - 22))
2
Step 2 :
Pulling out like terms :
3.1 Pull out like factors :
12x - 22 = 2 • (6x - 11)
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
12x - 22 = 2 • (6x - 11)
Equation at the end of step 3 :
(-4x - 2) + (6x - 11)
The Area of the platform is 33m²
Step-by-step explanation:
As the question says, the height of vertex from the base (D from AB) is 7m whereas the height of left vertex from the base (E from AB) is 4m
Thus it means the height of the Δ DCE (DX)= 7-4 ⇒3m
Since the platform is five-sided, the figure can be broken down into constituting parts
- Parallelogram ║ABCE
- Δ DCE
Are of the figure= Area of ║ABCE+ area Δ DCE
Area of ║ABCE= breadth * height
= 6*4 ⇒24m
²
Area Δ DCE= ½*(base)(height)
Putting the value of base is 6m and height as 3m
Area Δ DCE= ½*6*3
=9m
²
Total area= 24+9= 33m
²
Answer:
1, x = 80
2, z = 5.6
3, w = 18
Step-by-step explanation:
A regular trapezoid is shown in the picture attached.
We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5
Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:
AH = (AB - DC) ÷ 2
= (7 - 5) ÷ 2
= 2 ÷ 2
= 1
Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²)
= √(5² - 1²)
= √(25 - 1)
= √24
= 2√6
Last, we have all the information needed in order to calculate the area by the formula:

A = (7 + 5) × 2√6 ÷ 2
= 12√6
The area of the regular trapezoid is
12√6 square units.