5. Marc asked his mom to buy him a kite. Given that the area of a kite MARC is 96 cm? and one of the two diagonals measure 12 cm. Find the missing length of the other diagonal.
6. Crystal wants to travel to Palawan for 4 days and her suitcase that she brings form a trapezoid shape. Given that the two bases of this trapezoid are (2x + 4) inches and (7x+15) inches and the median is 23 inches. Find the value of x and the lengths of the given two bases.
7. William wants to buy earrings for her long-term girlfriend for their anniversary. The design of the earings that he bought forms a kite. Given that the two diagonals of earings are 13 mm and 6 mm. Find the area
8. Given that a dustpan is an isosceles trapezoid and its base angles are congruent. The measure of each angles are (6x+3)" and (7x-9). Find the value of x and the measures of the two base angles.
Answers & Comments
Sure, here is your answer to your question:
The area of a kite is equal to half the product of its diagonals. So, if the area of Marc's kite is 96 cm² and one of the diagonals measures 12 cm, then the other diagonal must measure 16 cm.
The median of a trapezoid is a line segment that connects the midpoints of two sides of the trapezoid. It is also parallel to the bases of the trapezoid and its length is equal to half the sum of the lengths of the bases. So, if the median of Crystal's suitcase is 23 inches and the two bases are (2x + 4) inches and (7x + 15) inches, then we can write the equation:
(2x + 4) + (7x + 15) = 46
9x + 19 = 46
9x = 27
x = 3
Therefore, the lengths of the two bases are 2(3) + 4 = 10 inches and 7(3) + 15 = 32 inches.
The area of a kite is equal to half the product of its diagonals. So, if the two diagonals of William's earrings are 13 mm and 6 mm, then the area of the earrings is:
(1/2)(13)(6) = 39 mm²
The sum of the angles of a trapezoid is 360°. Since the dustpan is an isosceles trapezoid, two of its angles are congruent and the other two angles are also congruent. So, if the measure of each base angle is (6x + 3)°, then the sum of the measures of the four angles is:
4(6x + 3) = 24x + 12
Since the sum of the angles of a trapezoid is 360°, we can set this equation equal to 360° and solve for x:
24x + 12 = 360
24x = 348
x = 14.5
Therefore, the measure of each base angle is (6)(14.5) + 3 = 93°.
I hope this helps! Let me know if you have any other questions.
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