Math

QuestionUn trapezio rettangolo ha basi che sommano a 96 cm96 \mathrm{~cm}. La base minore è 5/75/7 della maggiore. Trova l'area sapendo che l'altezza è 3/73/7 della base maggiore.

Studdy Solution

STEP 1

Assumptions1. The sum of the bases of a right trapezoid is96 cm. The smaller base is congruent to5/7 of the larger base3. The height of the trapezoid is3/7 of the larger base

STEP 2

First, we need to find the length of the larger base. We can do this by setting up an equation using the given information about the bases.
B+b=96cmB + b =96 \, cmwhere B is the larger base and b is the smaller base.

STEP 3

We know that the smaller base is congruent to5/7 of the larger base, so we can substitute this into the equation.
B+57B=96cmB + \frac{5}{7}B =96 \, cm

STEP 4

Combine like terms.
127B=96cm\frac{12}{7}B =96 \, cm

STEP 5

olve for B by multiplying both sides of the equation by the reciprocal of12/7, which is7/12.
B=712×96cmB = \frac{7}{12} \times96 \, cm

STEP 6

Calculate the value of B.
B=56cmB =56 \, cm

STEP 7

Now that we have the value of the larger base, we can find the value of the smaller base by multiplying the larger base by5/7.
b=57×Bb = \frac{5}{7} \times B

STEP 8

Substitute the value of B into the equation.
b=57×56cmb = \frac{5}{7} \times56 \, cm

STEP 9

Calculate the value of b.
b=40cmb =40 \, cm

STEP 10

Now that we have the values of the bases, we can calculate the height of the trapezoid by multiplying the larger base by3/7.
h=37×Bh = \frac{3}{7} \times B

STEP 11

Substitute the value of B into the equation.
h=37×56cmh = \frac{3}{7} \times56 \, cm

STEP 12

Calculate the value of h.
h=24cmh =24 \, cm

STEP 13

Now that we have the values of the bases and the height, we can calculate the area of the trapezoid using the formulaA=2(B+b)hA = \frac{}{2} (B + b) h

STEP 14

Substitute the values of B, b, and h into the equation.
A=2(56cm+40cm)×24cmA = \frac{}{2} (56 \, cm +40 \, cm) \times24 \, cm

STEP 15

Calculate the area of the trapezoid.
A=1152cm2A =1152 \, cm^2The area of the trapezoid is1152 square centimeters.

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