Quadrilaterals

Question 1

If a question asks for the sum of the degree of measures of the angles marked by the arrows? Once you calculate one arrow and the degree amount, what must you do?

Answer 1

Add the two together!

Question 2

What is the significance of a diagonal?

Question 3

If Rectangle DEFG has a diagonal of 13, what is it’s perimeter? It also have a width of 5

Answer 3

The diagonal divides the rectangle into two right triangles. Since one side of the triangle is 5 and the hypotenuse is 13, these are 5: 12: 13 right triangles. Add the lengths of all of the sides to find the perimeter and hence answer = 34

Question 4

QA: The area of a square with a perimeter of 40

QB: The area of a rectangle with a perimeter of 44

Answer 4

Answer = cannot be determined!!
A square is a subset of rectangles and therefore QB can follow the rules of a rectangle or it can follow the rules of a square and therefore the answer can’t be determined

Question 5

If a circle with an area of 16 pi is inscribed in a rectangle, what is the area of the rectangle?

Answer 5

Answer = 64
Draw a figure. For a circle to be perfectly inscribed (touching all sides of) a rectangle, the rectangle has to be a square. The area of the circle is Area = pi r^2. So 16pi = pi r^2. Therefore, r = 4.

When figures overlap, find what they have in common. The side of a square is s, is equal to the diameter of the circle, d. So s = d = 2r = 2(4) = 8. The area of a square is A = s^2. Therefore the answer is 8^2 = 64.

Question 6

PQRS is a rectangle
x = 2y

QA: The area of PQRS

QB: The perimeter of PQRS

Answer 6

Answer = the relationship can’t be determined! A square is a form of rectangle.

Question 7

If you know that something is a square but they do not give you any side lengths or angles of the square

QA: The area of the square

QB: The length of a diagonal across the square

Answer 7

Answer = cannot be determined!!

plug in using FROZEN

if the length of a side of the sqaure is 1, the area is also 1 and the length of the diagonal would be sqrt(1)

Question 8

the greatest possible area of a rectangle occurs when the rectangle is what?

Answer 8

a square

Question 9

A rectangle is inscribed in a circle that has a radius of 7. Which of the following values could represent the area of the rectangle?

9
49
81
100
121
196

Answer 9

Answers = 9, 49, and 81

as long as the answer is less than 98 it works - 45 45 90 side length rules to calculate this