Question

example students in an art club are painting a design on a wall of their school. rodrigo paints the triangle shown. what is the area of the triangle? you can use a formula to find the area. use the side labeled 4 ft as the base. then the height is 3 ft. a = 1/2bh = 1/2(4)(3) = 1/2(12) = 6 the area of the triangle is 6 ft². 1 suppose the height of rodrigos triangle in the example is doubled. will the area of the triangle also double? explain how you know. 2 alita and her uncle repair the sail to their boat. the sail is shaped like a triangle as shown. what is the area of the sail? show your work.

Explanation:

Step1: Recall area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Analyze effect of height - doubling

Let the original base be $b$ and original height be $h$, so original area $A_1=\frac{1}{2}bh$. If the height is doubled to $2h$, the new area $A_2=\frac{1}{2}b(2h)=bh$. Since $A_2 = 2\times\frac{1}{2}bh=2A_1$, the area doubles.

Step3: Solve for sail - area

For the sail, use the base $b = 4$ m and height $h=3.7$ m. Substitute into the area formula: $A=\frac{1}{2}\times4\times3.7$. First, $4\times3.7 = 14.8$, then $\frac{1}{2}\times14.8 = 7.4$ m².

Answer:

1. Yes, the area will double. When the height of a triangle is doubled while the base remains the same, using the formula $A=\frac{1}{2}bh$, the new area is twice the original area.
2. The area of the sail is $7.4$ m².