Question

Directions: Illustrate and solve the following problems:

1. Two consecutive sides of a parallelogram measure 4 m and 9 m,
respectively. What is the perimeter of the parallelogram?
2.One diagonal of a square measure (2x + 4) in. If the other diagonal
measures 16 in, what is x?
3.Given trapezoid QRST with QR//TS and UV as the median. If mQR = 12cm and mUV = 24 cm, what is mUV?
4.An isosceles trapezoid with a diagonal that measures 42 cm and one legmeasures 23 cm. What is the length of the other diagonal?
5.Given kite HOPE with diagonals mHP = 10 cm and m0E = 18 cm. What isthe area of the kite?

Answer 1

1. The perimeter of a parallelogram is the sum of the lengths of all four sides. If two consecutive sides of a parallelogram measure 4 m and 9 m, respectively, then the other two sides must also measure 4 m and 9 m, respectively (since opposite sides of a parallelogram are equal in length). Therefore, the perimeter of the parallelogram is:

Perimeter = 4 m + 9 m + 4 m + 9 m = 26 m

So the perimeter of the parallelogram is 26 meters.

2. In a square, both diagonals are equal in length. If one diagonal measures (2x + 4) in and the other diagonal measures 16 in, then we can write:

2x + 4 = 16

Solving for x, we get:

x = 6

So the value of x is 6 inches.

3. In a trapezoid, the length of the median is equal to the average of the lengths of the two parallel sides. If QR is parallel to TS and mQR = 12 cm, then mTS must also be equal to 12 cm. Let x be the length of the base of the trapezoid.

Then, we have:

mUV = (mQR + mTS)/2

Substituting the given values, we get:

24 cm = (12 cm + 12 cm + x)/2

Simplifying, we get:

24 cm = (24 cm + x)/2

Multiplying both sides by 2, we get:

48 cm = 24 cm + x

Subtracting 24 cm from both sides, we get:

x = 24 cm

So the length of the base of the trapezoid is 24 cm, and the length of the median UV is 24 cm.

(If this isn't right, I'm sorry!)

4. In an isosceles trapezoid, the diagonals are equal in length. If one diagonal measures 42 cm and one leg measures 23 cm, then we can use the Pythagorean theorem to find the length of the other leg:

d^2 = l^2 + (b/2)^2

where d is the length of the diagonal, l is the length of each leg, and b is the length of the base. Substituting the given values, we get:

42^2 = 23^2 + (b/2)^2

Simplifying, we get:

b^2/4 = 42^2 - 23^2

b^2/4 = 1253

Multiplying both sides by 4, we get:

b^2 = 5012

Taking the square root of both sides, we get:

b = sqrt(5012) ≈ 70.77

So the length of the other diagonal is also 42 cm.

5. The area of a kite is equal to half the product of the lengths of its diagonals. If mHP = 10 cm and mOE = 18 cm, then we can write:

Area = (mHP x mOE)/2

Substituting the given values, we get:

Area = (10 cm x 18 cm)/2 = 90 cm^2

So the area of the kite is 90 square centimeters.

I hope this helps! I'm sorry if this was wrong. If you need more help, ask me! :]