Answer:
128.8 cm²
Step-by-step explanation:
In the image attached below, the regular polygon is a square which is composed of a small square and a large square. In a square, all the sides are equal.
For the small square, half of the diagonal is 4 cm, therefore the length of the diagonal is 8 cm (2 × 4 cm). Let the length of the side be a cm, using Pythagoras theorem:
a² + a² = 8²
2a² = 64
a² = 32
a = √32 = 5.7 cm
The area of the small square = length × length = 5.7 × 5.7 = 32.5 cm²
For the large square, half of the diagonal is 9 cm, therefore the length of the diagonal is 18 cm (2 × 9 cm). Let the length of the side be b cm, using Pythagoras theorem:
b² + b² = 18²
2b² = 324
b² = 162
b = √162 = 12.7 cm
The area of the large square = length × length = 12.7 × 12.7 = 161.3 cm²
The area of the shaded region = Area of large square - Area of small square = 161.3 cm² - 32.5 cm² = 128.8 cm²
3 keep our signs. if dan has a board that is 15/16 yd and each is 2.5/8 (half of the original which is actually 5/16) then you can fit 3 signs
Answer:
t = 32
Step-by-step explanation:
The given equation is :
....(1)
Where
t is the number of guests attending the catered event.
The reciprocal of 
is 
.
Multiplying both sides by the reciprocal of .
Hence, 32 guests will attend the catered.
Answer:
3 5/6 + (-11/6) --> 2 2/3
Step-by-step explanation:
Step 1: 3-1--> 2
Step 2: 5/6 - 1/6 --> 2/3
Final Answ. : 2 2/3
Answer:
see explanation
Step-by-step explanation:
The nth term of a geometric progression is
= a₁
where a₁ is the first term and r the common ratio
Given a₅ = 162 and a₈ = 4374 , then
a₁
= 162 → (1)
a₁
= 4374 → (2)
Divide (2) by (1)
= 
r³ = 27
r = ![\sqrt[3]{27}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D)
= 3
Substitute r = 3 into (1) and solve for a₁
a₁
= 162
81a₁ = 162
a₁ = 
= 2
Then
a₂ = a₁ × 3 = 2 × 3 = 6
a₃ = a₂ × 3 = 6 × 3 = 18
The first 3 terms are 2, 6, 18
(ii)
The sum to n terms of a geometric progression is
= 
, then
= 
= 
= 59049 - 1
= 59048
