Answer:
10 ft
Step-by-step explanation:
area of trapezoid = (B + b)h/2
where B and b are the lengths of the bases, and h is the height.
A = (B + b)h/2
115 = (19 + 4)h/2
230 = 23h
23h = 230
h = 10
Answer: 10 ft
The height of the trapezoid with base lengths of 4 and 19 feet and an area of 115 square feet is 10 feet.
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
The area of a trapezoid is given as half of the product of the height(altitude) of the trapezoid and the sum of the length of the parallel sides.
[tex]\rm{ Area\ of\ trapezoid = \dfrac{1}{2} \times Height \times(Sum\ of\ parallel\ sides)[/tex]
The area of a trapezoid is given as half the product of the sum of the parallel sides and the height of the trapezoid.
The length of the parallel sides of the trapezoid is 4 and 19 feet, while the area of the trapezoid is 115 square feet. Therefore, the height of the trapezoid is,
115 ft² = 0.5 × (4 ft + 19 ft ) × height
115 ft² = 0.5 × 23 ft × height
height = (115 ft²)/ (0.5 × 23 ft)
height = 10 feet
Hence, the height of the trapezoid is 10 feet.
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