Answer:
25. The area of the trapezoid is 96 cm² ⇒ 2nd answer
26. The area of the kite is 40.8 feet² ⇒ 3rd answer
31. The area of the circle is 6.0025π m² ⇒ 3rd answer
Step-by-step explanation:
* Lets solve the problems
25. The figure is trapezoid
- The trapezoid has two parallel bases base 1 and base 2
- The area of the trapezoid is 1/2(base 1 + base 2) × height
- The length of base 1 is 12 cm
- The length of its height is 6 cm
- The length of the base 2 is (2 + 12 + the adjacent side to ∠45°)
- To find the missing part in the base 2 use the trigonometry
function tan 45° = opposite/adjacent
∵ tan 45° = opposite/adjacent
∵ The opposite = 6
∵ tan 45° = 1
∴ 1 = 6/adjacent ⇒ by using cross multiplication
∴ The adjacent = 6 cm
∴ The length of base 2 = 2 + 12 + 6 = 20 cm
∵ The area of the trapezoid is 1/2(base 1 + base 2) × height
∵ The length of base 1 = 12 cm
∵ The length of base 2 = 20 cm
∵ The length of its height = 6 cm
∴ The area = 1/2(12 + 20) × 6 = 1/2(32) × 6 = 16 × 6 = 96 cm²
* The area of the trapezoid is 96 cm²
26. The figure is kite
- The kite has two diagonals
- Its diagonals perpendicular to each other
- The longest diagonal bisects the shortest diagonal
- The area of the kite is 1/2(diagonal 1 × diagonal 2)
∵ The length of diagonal 1 = 10.2 feet
∵ The length of diagonal 2 = 8 feet
∵ The area of the kite = 1/2(diagonal 1 × diagonal 2)
∴ The area = 1/2(10.2 × 8) = 1/2(81.6) = 40.8 feet²
* The area of the kite is 40.8 feet²
31. The figure is a circle
- The circle has diameter
- The radius is half the diameter
- The area of the circle is π r²
∵ The length of the diameter = 4.9 m
∵ The length of the radius 1/2 the length of the diameter
∴ The length of the radius = 1/2 (4.9) = 2.45 m
∵ The area of the circle = π r²
∴ The area = π (2.45)² = 6.0025π m²
* The area of the circle is 6.0025π m²
