Question

area formulas, where b is the base and h is the height:
rectangle: a = bh (or a = lw)
square: a = bh (or a = s²)
parallelogram: a = bh
triangle: a = ½bh
1 a parallelogram has a base of 26 centimeters and an area of 182 square centimeters. what is the height?
a. 7 cm b. 156 cm
c. 676 cm d. 4,732 cm
2 john buys a flag folded in the shape of a triangle. the base of the triangle is 16 inches and the height is 17 inches. what is the area of the folded flag?
a. 136 in.² b. 163 in.²
c. 172 in.² d. 272 in.²
3 what is the area of the composite figure?
a. 120 m² b. 108 m²
c. 96 m² d. 84 m²
4 a rectangular yoga mat is 24 inches wide and 72 inches long. what is the area of the mat?
a. 48 in.² b. 96 in.²
c. 148 in.² d. 1,728 in.²
5 maria has a frame with an area of 85 square centimeters. based only on area, which two shapes fit inside her frame?
a. square with a side length of 42 cm
b. triangle with 12 - cm base and 14 - cm height
c. rectangle with 6 - cm base and 15 - cm height
d. rectangle with 7 - cm base and 14 - cm height
e. triangle with 13 - cm base and 14 - cm height
f. parallelogram with 6 - cm base and 14 - cm height
6 angela creates a quilt that is 8.5 feet long and 7 feet wide. the patches she uses are 1 foot by 1 foot. how many patches does angela use in her quilt?
a. 56 patches b. 56.5 patches
c. 59.5 patches d. 60 patches
7 sam has a graph paper notebook that is 26 centimeters by 20 centimeters. each square on the graph paper has an area of 1 square centimeter. how many squares are on each page of sams notebook?
a. 520 squares b. 530 squares
c. 540 squares d. 550 squares
8 a rectangular plot of land is set aside for a pool. the plot has a width of 22 feet and an area 638 square feet. which two pools, with the given dimensions, fit in the available plot of land?
a. 18 ft × 33 ft
b. 19 ft × 24 ft
c. 20 ft × 30 ft
d. 21 ft × 25 ft
e. 21 ft × 31 ft
f. 23 ft × 24 ft

Explanation:

Step1: Calculate the area of each shape

• Option A (square):

Using the formula \(A = s^{2}\), where \(s = 42\) cm.
\(A=42\times42 = 1764\) \(cm^{2}\)

• Option B (triangle):

Using the formula \(A=\frac{1}{2}bh\), where \(b = 12\) cm and \(h = 14\) cm.
\(A=\frac{1}{2}\times12\times14=6\times14 = 84\) \(cm^{2}\)

• Option C (rectangle):

Using the formula \(A = bh\) (or \(A=lw\)), where \(b = 6\) cm and \(h = 15\) cm.
\(A=6\times15=90\) \(cm^{2}\)

• Option D (rectangle):

Using the formula \(A = bh\) (or \(A=lw\)), where \(b = 7\) cm and \(h = 14\) cm.
\(A=7\times14 = 98\) \(cm^{2}\)

• Option E (triangle):

Using the formula \(A=\frac{1}{2}bh\), where \(b = 13\) cm and \(h = 14\) cm.
\(A=\frac{1}{2}\times13\times14=6.5\times14=91\) \(cm^{2}\)

• Option F (parallelogram):

Using the formula \(A = bh\), where \(b = 6\) cm and \(h = 14\) cm.
\(A=6\times14 = 84\) \(cm^{2}\)

Step2: Compare the areas with the frame's area

The frame has an area of \(85\) \(cm^{2}\).
We are looking for shapes with an area less than or equal to \(85\) \(cm^{2}\).

Answer:

B. triangle with 12 - cm base and 14 - cm height, F. parallelogram with 6 - cm base and 14 - cm height