Respuesta :
To answer this, you will find the sum of the bases by using the area of a trapezoid formula:
A = 1/2 x h x (b1 + b2) - You will represent the area of the 2 bases as x, because it says the sum of the bases so this can be
written as 1 term, x
69.6 = 1/2 x 8.7 x (x); solve for x
69.6 = 4.35x; divide both sides by 4.35
x = 16 in.
If 16 inches is the sum of the 2 bases and the sum of the legs, than you will double this answer to find the perimeter.
16 in x 2 = 32 inches
The perimeter is 32 inches.
A = 1/2 x h x (b1 + b2) - You will represent the area of the 2 bases as x, because it says the sum of the bases so this can be
written as 1 term, x
69.6 = 1/2 x 8.7 x (x); solve for x
69.6 = 4.35x; divide both sides by 4.35
x = 16 in.
If 16 inches is the sum of the 2 bases and the sum of the legs, than you will double this answer to find the perimeter.
16 in x 2 = 32 inches
The perimeter is 32 inches.
To solve such problems we must know about trapezoids.
Trapezoid
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.
Area of Trapezoid
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 perimeter of the trapezoid is 32 in..
Given to us
- The area of a trapezoid is 69.6 in²,
- Altitude(Height) is 8.7 in.,
- the sum of its legs is equal to the sum of its bases.
Area of Trapezoid
[tex]\rm{ Area\ of\ trapezoid = \dfrac{1}{2} \times Height \times(Sum\ of\ parallel\ sides)[/tex]
[tex]\rm{ 69.6\ in.^2 = \dfrac{1}{2} \times 8.7 \times (Sum\ of\ parallel\ sides)[/tex]
[tex]\rm{ (Sum\ of\ parallel\ sides)=\dfrac{69.6 \times 2}{8.7}[/tex]
[tex]\rm{ (Sum\ of\ parallel\ sides)=\dfrac{69.6 \times 2}{8.7}[/tex]
[tex]\rm{ (Sum\ of\ parallel\ sides)=16[/tex]
According to the Statement
sum of its legs is equal to the sum of its bases. therefore,
sum of its legs = sum of its bases.
sum of its legs = sum of parallel sides
sum of its legs = 16 in
Perimeter of the trapezoid
Perimeter of the trapezoid = Sum of all sides
= sum of its legs + sum of its bases
= 16 in. + 16 in.
= 32 in.
Hence, the perimeter of the trapezoid is 32 in.
Learn more about Trapezoid:
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