Question

Help me ;v; and thank you sm!

Answer 1

27 Cm² (C)

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Answer 2

Answer:  Choice C.   27 cm^2

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Explanation:

It's not directly stated, but I'm assuming that there's symmetry going on in terms of the triangle on the left being a mirror copy of the triangle on the right. If that assumption is true, then we have another "3 cm" along the bottom edge. In total, the bottom edge is 3+6+3 = 12 cm long.

The top edge, parallel to the bottom one, is 6 cm. We'll denote the two parallel sides to be the base lengths and we could write $b_1 = 6 \text{ and } b_2 = 12$. The small subscript just helps us differentiate between the two base lengths.

The height is the vertical dashed line of 3 cm. This means h = 3. The height is always perpendicular to the base.

We'll plug those three variables into the area of a trapezoid formula below

$A = \frac{h*(b_1+b_2)}{2}\\\\A = \frac{3*(6+12)}{2}\\\\A = \frac{3*(18)}{2}\\\\A = \frac{54}{2}\\\\A = 27$

The area is 27 square cm

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Another way to get the answer is to break the trapezoid into three pieces: two triangles and a rectangle in between.

One triangle has an area of base*height/2 = 3*3/2 = 9/2 = 4.5 square cm, which means two triangles combine to an area of 2*4.5 = 9 square cm.

The rectangle has area of length*width = 6*3 = 18 cm^2

The trapezoid's area is the combination of what we found: 9+18 = 27 cm^2