Area of Triangles and Trapezoids + Area of Circles + Composite Figures

https://internationalvla.owschools.com/media/g_mat08_ccss_2016/7/img_triangle_within_circle.gif A triangular flowerbed is being planted inside a circular area of grass. What is the area of the grass (the area surrounding the flowerbed)? (Use 3.14 for π.)

1,965.74 ft^2

https://internationalvla.owschools.com/media/g_mat08_ccss_2016/7/img_trapezoid_1.gif Find the area of the following trapezoid.

14 ft^2

The area of a trapezoid is 144 ft 2. If the height is 8 feet and one of the bases is 12 feet, what is the length of the other base?

24 ft How to solve: First, since know the formula to solve the area of a trapezoid is 1/2(b1 + b2) * h, we can do the opposite. Take 144 and multiply it by two, which gives you 288. Then, take 288 and divide it by 8, which gives you 36. Then, subtract 12 from 36 which gives you 24. The answer to the problem is 24 ft

Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches, by what factor was the first rectangle changed?

3

Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches, how much longer is the second rectangle's perimeter?

3 times as long

A rhombus is enlarged and has a new perimeter of 40 feet. If the original perimeter was 10 feet, by what factor was the rhombus enlarged?

4

If a circle is enlarged so that it has a new area that is 25 times the original, what factor were the dimensions changed by?

5

https://internationalvla.owschools.com/media/g_mat08_ccss_2016/7/img_composite_figure_6.gif What is the area of the shaded region of the following figure?

5,274 in^2

A parallelogram has an area of 14 cm 2. If the dimensions of the parallelogram are doubled, what will the new area be?

56 cm^2

What is the area of a triangle that has a base of 3 feet and a height of 6 feet?

9 ft^2

Two rectangles are similar. If the height of the first rectangle is 3 inches, and the height of the second rectangle is 9 inches, how much larger is the second rectangle's area?

9 times as large

Area of a Triangle Formula

A = 1/2 * b * height

Area of a Trapezoid Formula

A = 1/2(b1 + b2) * h

For a game, Tony has a rectangle drawn on a piece of paper that has an area of 18 in^2. What should he do to the dimensions in order to have a similar rectangle that's area is only 2 in^2?

Divide them by three.

A circle that originally had a circumference of 31.4 cm, now has a circumference of 15.7 cm. What happened to the radius?

It was divided by two.

A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle?

increased by a factor of 4

If the dimensions of a circle are increased by a factor of 3 (tripled), how will the area of the circle be affected?

increased by a factor of 9

The dimensions of a parallelogram are reduced by half of its original dimensions. Determine how the perimeter of the parallelogram will be affected by the change in the dimensions of the original parallelogram.

reduced by a factor of one-half