Bianca needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Two right triangles are attached along their longest side. The smaller triangle has height 6 cm and base 2 cm. The height of the larger triangle is 7 cm and its base is 3 cm.
(1 point)
1.0 cm2
4.5 cm2
9.0 cm2
16.5 cm2
How do you know
A1 = (1/2) *6 * 2 = 6
A2 = (1/2) *7 * 3 = 10.5
A2 - A1 = 4.5
To find the difference between the area of the large triangle and the small triangle, we first need to calculate the area of each triangle separately.
The formula to calculate the area of a triangle is: Area = (base * height) / 2.
Let's calculate the area of the small triangle:
Area of small triangle = (base * height) / 2
= (2 cm * 6 cm) / 2
= (12 cm²) / 2
= 6 cm²
Now, let's calculate the area of the large triangle:
Area of large triangle = (base * height) / 2
= (3 cm * 7 cm) / 2
= (21 cm²) / 2
= 10.5 cm²
Now, to find the difference between the area of the large triangle and the small triangle, we subtract the area of the small triangle from the area of the large triangle:
Difference = Area of large triangle - Area of small triangle
= 10.5 cm² - 6 cm²
= 4.5 cm²
Therefore, the difference between the area of the large triangle and the area of the small triangle is 4.5 cm².
So, the answer is 4.5 cm².