15. scott and tara were asked to find the
area of this trapezoid:
16 cm
18 cm
24 cm
scott wrote a = 2(24 + 16)(8).
tara wrote a = (16 + 24)(8)
which student is correct? explain.

Both Scott and Tara have responded correctly.

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

A=(1/2)[b1+b2]h

we have

b1=16 cm

b2=24 cm

h=8 cm > Note The height is 8 cm instead of 18 cm

substitute

A=(1/2)[16+24](8)

A=160 cm²

Verify Scott 's work

Note Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)

Remember that the Commutative Property establishes "The order of the addends does not alter its result"

so

(24+16)=(16+24)

A = (1/2)(24 + 16)(8)=160 cm²

Verify Tara's work

Note Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)

A = (1/2)(16+24)(8)=160 cm²