Question

topic 10 block 6 homework name

1. johnson middle school is planning a new recreation area for the community. part of the area will be shaded triangular sunshades. ximena measures the distances between the poles that will hold the sunshade and finds that the triangular sunshade will need a base of 78 inches and a height of 67.5 inches.

the area of fabric needed for the sunshade is ______ square inches.
the fabric is sold in square feet.
the base of the triangle is ____ feet and the height of the triangle is ____ feet.
the area of fabric needed for the sunshade is about ______ square feet.

1. the picnic table area in the new recreation area will be covered with woodchips, also called mulch. the diagram shows the mulched area shaded in pink. it will also be mulched under the green tables. use the diagram to find the mulched area.

a. $96\\ ft^2$ b. $24\\ ft^2$
c. $160\\ ft^2$ d. $40\\ ft^2$
e. $108\\ ft^2$

1. part of the blacktop must be replaced in the parking lot. in the diagram, the blacktop that will be replaced is shaded in green.

estimate the area of asphalt needed to fill in the shape.
a. $20\\ ft^2$
b. $25\\ ft^2$
c. $16\\ ft^2$
d. $12\\ ft^2$

Explanation:

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Problem 1

Step1: Calculate area in sq inches

Area of triangle: $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 78 \times 67.5$

Step2: Convert base to feet

$\text{Base (ft)} = \frac{78}{12}$

Step3: Convert height to feet

$\text{Height (ft)} = \frac{67.5}{12}$

Step4: Calculate area in sq feet

$\text{Area (sq ft)} = \frac{1}{2} \times 6.5 \times 5.625$

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Problem 2

Step1: Count total grid squares

Count full/partial squares: 25 total squares

Step2: Calculate total mulch area

$\text{Total Area} = 25 \times 4$

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Problem 3

Step1: Count full/approx squares

Count shaded squares: ~16 total squares

Step2: Match to option

Area = $16 \times 1$

Answer:

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Problem 1:

The area of fabric needed for the sunshade is $\boldsymbol{2632.5}$ square inches.
The base of the triangle is $\boldsymbol{6.5}$ feet and the height of the triangle is $\boldsymbol{5.625}$ feet.
The area of fabric needed for the sunshade is about $\boldsymbol{18.28}$ square feet.

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Problem 2:

$\boldsymbol{c. 160\ ft^2}$

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Problem 3:

$\boldsymbol{c. 16\ ft^2}$