Find the area of the following shape. Use Use pi=3.142 and give your answer correct to 1 decimal place.

Question

Find the area of the following shape. Use Use pi=3.142 and give your answer correct to 1 decimal place.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

Q1: Find the area of the following shape. Use $\pi=3.142$ and give your answer correct to 1 decimal place.

Calculate the area of the rectangular part.
The rectangle has a length of 16 cm and a width of 7 cm.
$\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 16\, \text{cm} \times 7\, \text{cm} = 112\, \text{cm}^2$
Calculate the area of the semicircular part.
The diameter of the semicircle is 7 cm, so the radius is $r = \frac{7}{2} = 3.5$ cm.
$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.142 \times (3.5\, \text{cm})^2$ $\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 3.142 \times 12.25\, \text{cm}^2 = 19.24925\, \text{cm}^2$
Add the areas to find the total area and round to one decimal place.
$\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}} = 112\, \text{cm}^2 + 19.24925\, \text{cm}^2 = 131.24925\, \text{cm}^2$
Rounding to one decimal place:
$\text{Total Area} \approx 131.2\, \text{cm}^2$
The final answer is $\boxed{\text{131.2 cm}^2}$ .

Q2: Find the area of the shaded region. Give your answer to the nearest cm².
Calculate the area of the large rectangle.
The rectangle has a length of 44 cm and a width of 28 cm.
$\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 44\, \text{cm} \times 28\, \text{cm} = 1232\, \text{cm}^2$
Calculate the area of the unshaded triangle.
The triangle has a base of 34 cm and a height of 18 cm.
$\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 34\, \text{cm} \times 18\, \text{cm} = 306\, \text{cm}^2$
Subtract the area of the triangle from the area of the rectangle to find the shaded area and round to the nearest cm².
$\text{Area}_{\text{shaded}} = \text{Area}_{\text{rectangle}} - \text{Area}_{\text{triangle}} = 1232\, \text{cm}^2 - 306\, \text{cm}^2 = 926\, \text{cm}^2$
The final answer is $\boxed{\text{926 cm}^2}$ .

Q3: Find the area of the following trapezium (correct to 2 decimal places).
Identify the lengths of the parallel sides and the height.
The parallel sides are $a = 5.54$ cm and $b = 7.64$ cm.
The height is $h = 3.9$ cm.
Use the formula for the area of a trapezium.
The area of a trapezium is given by $\text{Area} = \frac{1}{2} (a+b) h$ .
$\text{Area} = \frac{1}{2} (5.54\, \text{cm} + 7.64\, \text{cm}) \times 3.9\, \text{cm}$ $\text{Area} = \frac{1}{2} (13.18\, \text{cm}) \times 3.9\, \text{cm}$ $\text{Area} = 6.59\, \text{cm} \times 3.9\, \text{cm} = 25.701\, \text{cm}^2$
Round the answer to two decimal places.
$\text{Area} \approx 25.70\, \text{cm}^2$
The final answer is $\boxed{\text{25.70 cm}^2}$ .

Q4: Find the surface area of the Triangular prism.
Calculate the area of the two triangular bases.
The base of the triangle is $B = 35$ and the height is $H = 28$ .
$\text{Area}_{\text{base triangle}} = \frac{1}{2} \times B \times H = \frac{1}{2} \times 35 \times 28 = 490$
Since there are two such bases, their combined area is $2 \times 490 = 980$ .
Calculate the areas of the three rectangular faces.
The length of the prism is $L = 25$ . The sides of the triangular base are 35, 33, and 33 (from the diagram, assuming the $S=33$ refers to the equal sides of the isosceles triangle, which is consistent with $\sqrt{28^2 + (35/2)^2} \approx 33$ ).
- Area of the bottom rectangular face: $35 \times 25 = 875$
- Area of the first slanted rectangular face: $33 \times 25 = 825$
- Area of the second slanted rectangular face: $33 \times 25 = 825$
Sum all the areas to find the total surface area.
$\text{Total Surface Area} = (2 \times \text{Area}_{\text{base triangle}}) + \text{Area}_{\text{face 1}} + \text{Area}_{\text{face 2}} + \text{Area}_{\text{face 3}}$ $\text{Total Surface Area} = 980 + 875 + 825 + 825 = 3505$
The units are not specified in the question or diagram for this problem, so we will assume generic units.
The final answer is $\boxed{\text{3505 square units}}$ .

Q5: Find the Total surface area of the following closed cone with the following dimensions: $r=9$ , $H=18$ , $L=20$ . Use $\pi=3.14$ and give your answer to the nearest square units.
Identify the given dimensions.
Radius $r = 9$ .
Slant height $L = 20$ .
Height $H = 18$ .
Use $\pi = 3.14$ .
Calculate the area of the circular base.
$\text{Area}_{\text{base}} = \pi r^2 = 3.14 \times (9)^2 = 3.14 \times 81 = 254.34$
Calculate the lateral surface area of the cone.
$\text{Area}_{\text{lateral}} = \pi r L = 3.14 \times 9 \times 20 = 3.14 \times 180 = 565.2$
Add the base area and lateral surface area to find the total surface area and round to the nearest square unit.
$\text{Total Surface Area} = \text{Area}_{\text{base}} + \text{Area}_{\text{lateral}} = 254.34 + 565.2 = 819.54$
Rounding to the nearest square unit:
$\text{Total Surface Area} \approx 820$
The final answer is $\boxed{\text{820 square units}}$ .

Find the area of the following shape. Use Use pi=3.142 and give your answer correct to 1 decimal place.

Step-by-step solution

Calculate the area of the rectangular part.

Calculate the area of the semicircular part.

Add the areas to find the total area and round to one decimal place.

Calculate the area of the large rectangle.

Calculate the area of the unshaded triangle.

Subtract the area of the triangle from the area of the rectangle to find the shaded area and round to the nearest cm².

Identify the lengths of the parallel sides and the height.

Use the formula for the area of a trapezium.

Round the answer to two decimal places.

Calculate the area of the two triangular bases.

Calculate the areas of the three rectangular faces.

Sum all the areas to find the total surface area.

Identify the given dimensions.

Calculate the area of the circular base.

Calculate the lateral surface area of the cone.

Add the base area and lateral surface area to find the total surface area and round to the nearest square unit.

Still stuck on this one?

More Mathematics Questions

Find the area of the following shape. Use Use pi=3.142 and give your answer correct to 1 decimal place.

Step-by-step solution

Calculate the area of the rectangular part.

Calculate the area of the semicircular part.

Add the areas to find the total area and round to one decimal place.

Calculate the area of the large rectangle.

Calculate the area of the unshaded triangle.

Subtract the area of the triangle from the area of the rectangle to find the shaded area and round to the nearest cm².

Identify the lengths of the parallel sides and the height.

Use the formula for the area of a trapezium.

Round the answer to two decimal places.

Calculate the area of the two triangular bases.

Calculate the areas of the three rectangular faces.

Sum all the areas to find the total surface area.

Identify the given dimensions.

Calculate the area of the circular base.

Calculate the lateral surface area of the cone.

Add the base area and lateral surface area to find the total surface area and round to the nearest square unit.

Still stuck on this one?

More Mathematics Questions

Find the area of the following shape. Use Use pi=3.142 and give your answer correct to 1 decimal place.