How to find the area of a trapezoid - SAT Math
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A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?
A trapezoid has a base of length 4, another base of length s, and a height of length s. A square has sides of length s. What is the value of s such that the area of the trapezoid and the area of the square are equal?
In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:
area of trapezoid = (1/2)(4 + s)(s)
Similarly, the area of a square with sides of length a is given by _a_2. Thus, the area of the square given in the problem is _s_2.
We now can set the area of the trapezoid equal to the area of the square and solve for s.
(1/2)(4 + s)(s) = _s_2
Multiply both sides by 2 to eliminate the 1/2.
(4 + s)(s) = 2_s_2
Distribute the s on the left.
4_s_ + _s_2 = 2_s_2
Subtract _s_2 from both sides.
4_s_ = _s_2
Because s must be a positive number, we can divide both sides by s.
4 = s
This means the value of s must be 4.
The answer is 4.
In general, the formula for the area of a trapezoid is (1/2)(a + b)(h), where a and b are the lengths of the bases, and h is the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:
area of trapezoid = (1/2)(4 + s)(s)
Similarly, the area of a square with sides of length a is given by _a_2. Thus, the area of the square given in the problem is _s_2.
We now can set the area of the trapezoid equal to the area of the square and solve for s.
(1/2)(4 + s)(s) = _s_2
Multiply both sides by 2 to eliminate the 1/2.
(4 + s)(s) = 2_s_2
Distribute the s on the left.
4_s_ + _s_2 = 2_s_2
Subtract _s_2 from both sides.
4_s_ = _s_2
Because s must be a positive number, we can divide both sides by s.
4 = s
This means the value of s must be 4.
The answer is 4.
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Find the area of a trapezoid given bases of length 1 and 2 and height of 2.
Find the area of a trapezoid given bases of length 1 and 2 and height of 2.
To solve, simply use the formula for the area of a trapezoid. Thus,
To solve, simply use the formula for the area of a trapezoid. Thus,
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The above figure shows Square 
. 
is the midpoint of 
; 
is the midpoint of 
; 
is the midpoint of 
. Construct 
.
If Square 
has area 
, what is the area of Quadrilateral 
?
The above figure shows Square
If Square
Let 
be the common sidelength of the square. The area of the square is 
.
Construct segment 
. This divides the square into Rectangle 
and a right triangle. The dimensions of Rectangle 
are
and
.
The area of Rectangle 
s the product of these dimensions:
The lengths of the legs of Right 
are
and
The area of this right triangle is half the product of these lengths, or
This is seen below:
The sum of these areas is the area of Quadrilateral
.
Substituting 
for 
, the area is 
.
Let
Construct segment
and
The area of Rectangle
The lengths of the legs of Right
and
The area of this right triangle is half the product of these lengths, or
This is seen below:
The sum of these areas is the area of Quadrilateral
Substituting
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