What is the area of the trapezoid below?
What is the area of the trapezoid shown in the image linked below? The options for the area are as follows:
1. (36\sqrt{3} \, \text{cm}^2)
2. (44\sqrt{3} \, \text{cm}^2)
3. (65 \, \text{cm}^2)
4. (88 \, \text{cm}^2)
4 Answers
The longer base is 7 + 4= 11
We need the height, use the Pythagorean Thm.
4² + h² = 8²
16 + h² = 64
h² = 48
√h² = √(16 * 3)………√.N² = N
h = 4√3
A= 1/2 (sum of the bases) * height
A= 1/2(11 + 7)* 4√3
A = 1/2(18)* 4√3
A = 9* 4√3
A = 36√3 cm²
The bases are 7 & 11, so the average of the bases is 9
4^2 + h^2 = 8^2, so h = sqrt48 which is 4 sqrt3
The area of a trapezoid is the average of the bases times the height: 9 * 4sqrt 3 = 36sqrt3
The first one is the answer
The trapezoid consists of a triangle with sides 4cm and 8cm and a rectangle with one known side 7cm.
rectangle : the height of the rectangle can be found using a little help from Pythagoras
8² = x² + 4² –> x = 4sqrt(3) cm
So its area is: A1 = (4sqrt(3)cm)(7cm) = 28sqrt(3) cm²
triangle: area is A2 = (4sqrt(3))(4cm)/2 = 8sqrt(3) cm²
So answer number 1 is correct.
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