Question

area formulas, where ( b ) is the base and ( h ) is the height:
rectangle: ( a = bh ) (or ( a = lw ))
square: ( a = bh ) (or ( a = s^{2} ))
parallelogram: ( a = bh )
triangle: ( a = \frac{1}{2}bh )
1 a parallelogram has a base of 26 centimeters and an area of 182 square centimeters. what is the height?
a. ( 7 mathrm{~cm} )
b. ( 156 mathrm{~cm} )
c. ( 676 mathrm{~cm} )
d. ( 4,732 mathrm{~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 mathrm{in.}^{2} )
b. ( 163 mathrm{in.}^{2} )
c. ( 172 mathrm{in.}^{2} )
d. ( 272 mathrm{in.}^{2} )
3 what is the area of the composite figure?
a. ( 120 mathrm{~m}^{2} )
b. ( 108 mathrm{~m}^{2} )
c. ( 96 mathrm{~m}^{2} )
d. ( 84 mathrm{~m}^{2} )
4 a rectangular yoga mat is 24 inches wide and 72 inches long. what is the area of the mat?
a. ( 48 mathrm{in.}^{2} )
b. ( 96 mathrm{in.}^{2} )
c. ( 148 mathrm{in.}^{2} )
d. ( 1,728 mathrm{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 mathrm{~cm} )
b. triangle with ( 12-mathrm{cm} ) base and ( 14-mathrm{cm} ) height
c. rectangle with ( 6-mathrm{cm} ) base and ( 15-mathrm{cm} ) height
d. rectangle with ( 7-mathrm{cm} ) base and ( 14-mathrm{cm} ) height
e. triangle with ( 13-mathrm{cm} ) base and ( 14-mathrm{cm} ) height
f. parallelogram with ( 6-mathrm{cm} ) base and ( 14-mathrm{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 mathrm{ft} \times 33 mathrm{ft} )
b. ( 19 mathrm{ft} \times 24 mathrm{ft} )
c. ( 20 mathrm{ft} \times 30 mathrm{ft} )
d. ( 21 mathrm{ft} \times 25 mathrm{ft} )
e. ( 21 mathrm{ft} \times 31 mathrm{ft} )
f. ( 23 mathrm{ft} \times 24 mathrm{ft} )

Explanation:

Step1: Calculate the area of each option

• 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 \(A = bh\), where \(b = 6\) cm and \(h = 15\) cm.
\(A=6\times15=90\) \(cm^{2}\)

• Option D (rectangle):

Using the formula \(A = bh\), 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.
\(A=\frac{1}{2}\times13\times14=13\times7=91\) \(cm^{2}\)

• 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 \(85\) \(cm^{2}\).
Options B (\(84\) \(cm^{2}\)) and F (\(84\) \(cm^{2}\)) have areas less than \(85\) \(cm^{2}\)

Answer:

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