Examkin

Soru

Zorluk: OrtaGeometric Figures on the Coordinate Plane

A kite has vertices K(2,8)K(2, 8), I(6,3)I(6, 3), T(2,−4)T(2, -4), and E(−2,3)E(-2, 3) in the standard (x,y)(x, y) coordinate plane. What is the area of kite KITEKITE, in square units?

Cevap: 48 square units

Cevap

The area of kite KITEKITE is 48 square units.
The area of kite KITEKITE is 48 because the horizontal diagonal IEIE has a length of 8 units, the vertical diagonal KTKT has a length of 12 units, and the area of a kite is calculated as half the product of its diagonal lengths: 12×8×12=48\frac{1}{2} \times 8 \times 12 = 48.

Adım Adım Çözüm

1
Calculate the lengths of the vertical diagonal KTKT and the horizontal diagonal IEIE.
The length of KTKT is 12 and the length of IEIE is 8.
The vertices K(2,8)K(2, 8) and T(2,−4)T(2, -4) share the same xx-coordinate, so the diagonal is vertical with length 8−(−4)=128 - (-4) = 12. The vertices I(6,3)I(6, 3) and E(−2,3)E(-2, 3) share the same yy-coordinate, so the diagonal is horizontal with length 6−(−2)=86 - (-2) = 8.
2
Apply the area formula for a kite: Area=12d1d2\text{Area} = \frac{1}{2} d_1 d_2.
Area = 48
Since the diagonals of a kite are perpendicular, the area is half the product of the lengths of the diagonals: 12×12×8=48\frac{1}{2} \times 12 \times 8 = 48.

Anahtar Kavram

Finding the area of a geometric figure on the coordinate plane by using diagonal lengths.
Bu soruyu puanla

Konular

Geometric Figures on the Coordinate Plane

Bu konudan daha fazla soru