(Please check the attachment for the diagram which will support the answer)
The regular pentagon is made up of five triangles as shown in the diagram. Let us now take the case of the bottom triangle ODC. We know from basic geometry that the area of any triangle is half times base times height. So, the area of the triangle will be half times DC (which is the base) times OP (which is the height).
Now, if we take into account all the triangles that make the pentagon we will get similar areas. The height of all such triangles will remain the same as OP because this is a regular pentagon.
Adding all these areas will give us the area of the pentagon which will come out to be:
Area of Pentagon=Area of Triangle OCD + Area of Triangle OBC +Area of Triangle OAB + Area of Triangle OAE + Area of Triangle OED
(Please see attachments for complete solution)
As we can see from the last attachment, the sum in the parenthesis is the perimeter of the pentagon and thus we get the area of the pentagon as
1/2 times apothem times Perimeter
Answer:
7
Step-by-step explanation:
it's a rectangle of area 2*4=8 minus a triangle of area 1*2/2=1 so 8 - 1 = 7
Answer:
B. 455
Step-by-step explanation:
The order in which the toppings are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
3 toppings from a set of 15. So
455 3-topping sundaes can be made.
1) 32% students chose red, yellow, & orange.
Find the total number of students that gave their favorite color.
6 + 4 + 8 + 7 + 9 + 3 + 4 + 9 = 50 students
Find the students that chose red, yellow, and orange.
9 + 4 + 3 = 16
16 out of 50 students chose red, yellow, & orange as their favorite color.
16/50 = 32/100, which is 32%.
2) No, 2/25 students chose pink, which is less than 1/10.
Find the number of students that chose pink -- 4 students. 4 out of 50 students. 4/50 reduced is 2/25.
2/25 is 0.08.
1/10 is 0.10.
So, less than 1/10 of the students chose pink as their favorite color.
3) 18% students chose blue as their favorite color.
Find how many students chose blue -- 9 students.
9 students out of 50 students, 9/50. Multiply both sides by 2 to get 18/100.
18/100 is 18 percent.
4) 21/50 students chose green, black, & purple.
Find how many students chose green, black, and purple.
7 + 8 + 6 = 21
21 out of 50 students, 21/50.
Answer:
185
Step-by-step explanation:
14.8 / 0.08 = 185
Best of Luck!