Question

A triangle has a base of 8 cm and a height of 3 cm. The triangle is dilated by a scale factor of 3. Calculate and compare the areas of the dilated triangle and the original triangle.

(1 point)
Responses

The original triangle has an area of 12 cm2
and the dilated triangle has an area of 108 cm2
; therefore, the dilated triangle has an area 9 times the size of the original triangle.
The original triangle has an area of 12 cm squared and the dilated triangle has an area of 108 cm squared ; therefore, the dilated triangle has an area 9 times the size of the original triangle.

The original triangle has an area of 24 cm2
and the dilated triangle has an area of 36 cm2
; therefore, the dilated triangle has an area 1.5 times the size of the original triangle.
The original triangle has an area of 24 cm squared and the dilated triangle has an area of 36 cm squared ; therefore, the dilated triangle has an area 1.5 times the size of the original triangle.

The original triangle has an area of 12 cm2
and the dilated triangle has an area of 36 cm2
; therefore, the dilated triangle has an area 3 times the size of the original triangle.
The original triangle has an area of 12 cm squared and the dilated triangle has an area of 36 cm squared ; therefore, the dilated triangle has an area 3 times the size of the original triangle.

The original triangle has an area of 24 cm2
and the dilated triangle has an area of 108 cm2
; therefore, the dilated triangle has an area 4.5 times the size of the original triangle.

Answer 1

Area = 1/2·base·height = 1/2·8·3 = 12 cm².
A dilation by scale factor 3 scales area by 3² = 9, so dilated area = 12·9 = 108 cm².
Therefore the first response is correct: original 12 cm², dilated 108 cm², dilated area is 9 times the original.