Math / Geometry

QuestionWhat is the surface area of the pyramid above? (A) $10 \mathrm{~m}^{2}$ (B) $40 \mathrm{~m}^{2}$ (C) $56 \mathrm{~m}^{2}$ (D) $80 \mathrm{~m}^{2}$

Studdy Solution

STEP 1

What is this asking? We need to find the total surface area of a pyramid, which means the area of the bottom square plus the area of the four triangle sides. Watch out! Don't forget that the pyramid has five sides in total: one square and four triangles!
Also, remember that the slant height is different from the pyramid's height.

STEP 2

1. Find the area of the square base.
2. Find the area of one triangular side.
3. Find the total area of the four triangular sides.
4. Calculate the total surface area.

STEP 3

The base is a square, and we know the side length is $4$ meters.
The area of a square is side multiplied by side.

STEP 4

So, the area of the base is $4 \cdot 4 = \textbf{16}$ square meters.
Write that down!

STEP 5

We know the base of each triangle is $4$ meters (same as the square).
We also know the slant height, which is like the triangle's height, is $5$ meters.
The area of a triangle is one-half base times height.

STEP 6

So, the area of one triangle is $\frac{1}{2} \cdot 4 \cdot 5 = \textbf{10}$ square meters.
Awesome!

STEP 7

Since there are four identical triangles, the total area of all the triangular sides is $4 \cdot 10 = \textbf{40}$ square meters.
We're almost there!

STEP 8

Now, we add the area of the square base (which was $\textbf{16}$ square meters) and the total area of the triangle sides (which was $\textbf{40}$ square meters).

STEP 9

So, the total surface area is $16 + 40 = \textbf{56}$ square meters.
Boom!

STEP 10

The total surface area of the pyramid is $56$ square meters, so the answer is (C).

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QuestionWhat is the surface area of the pyramid above? (A) $10 \mathrm{~m}^{2}$ (B) $40 \mathrm{~m}^{2}$ (C) $56 \mathrm{~m}^{2}$ (D) $80 \mathrm{~m}^{2}$

Studdy Solution

STEP 1

STEP 2

1. Find the area of the square base.
2. Find the area of one triangular side.
3. Find the total area of the four triangular sides.
4. Calculate the total surface area.

STEP 3

The base is a square, and we know the side length is $4$ meters.
The area of a square is side multiplied by side.

STEP 4

So, the area of the base is $4 \cdot 4 = \textbf{16}$ square meters.
Write that down!

STEP 5

We know the base of each triangle is $4$ meters (same as the square).
We also know the slant height, which is like the triangle's height, is $5$ meters.
The area of a triangle is one-half base times height.

STEP 6

So, the area of one triangle is $\frac{1}{2} \cdot 4 \cdot 5 = \textbf{10}$ square meters.
Awesome!

STEP 7

Since there are four identical triangles, the total area of all the triangular sides is $4 \cdot 10 = \textbf{40}$ square meters.
We're almost there!

STEP 8

Now, we add the area of the square base (which was $\textbf{16}$ square meters) and the total area of the triangle sides (which was $\textbf{40}$ square meters).

STEP 9

So, the total surface area is $16 + 40 = \textbf{56}$ square meters.
Boom!

STEP 10

The total surface area of the pyramid is $56$ square meters, so the answer is (C).

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QuestionWhat is the surface area of the pyramid above? (A) 10 m210 \mathrm{~m}^{2}10 m2 (B) 40 m240 \mathrm{~m}^{2}40 m2 (C) 56 m256 \mathrm{~m}^{2}56 m2 (D) 80 m280 \mathrm{~m}^{2}80 m2

Studdy Solution

STEP 1

STEP 2

1. Find the area of the square base.2. Find the area of one triangular side.3. Find the total area of the four triangular sides.4. Calculate the total surface area.

STEP 3

The base is a square, and we know the side length is 444 meters.The area of a square is side multiplied by side.

STEP 4

So, the area of the base is 4⋅4=164 \cdot 4 = \textbf{16}4⋅4=16 **square meters**.Write that down!

STEP 5

We know the base of each triangle is 444 meters (same as the square).We also know the **slant height**, which is like the triangle's height, is 555 meters.The area of a triangle is one-half base times height.

STEP 6

So, the area of *one* triangle is 12⋅4⋅5=10\frac{1}{2} \cdot 4 \cdot 5 = \textbf{10}21​⋅4⋅5=10 **square meters**.Awesome!

STEP 7

Since there are four identical triangles, the total area of all the triangular sides is 4⋅10=404 \cdot 10 = \textbf{40}4⋅10=40 **square meters**.We're almost there!

STEP 8

Now, we **add** the area of the square base (which was 16\textbf{16}16 square meters) and the total area of the triangle sides (which was 40\textbf{40}40 square meters).

STEP 9

So, the total surface area is 16+40=5616 + 40 = \textbf{56}16+40=56 **square meters**.Boom!

STEP 10

The total surface area of the pyramid is 565656 square meters, so the answer is (C).

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Studdy solves anything!

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QuestionWhat is the surface area of the pyramid above? (A) $10 \mathrm{~m}^{2}$ (B) $40 \mathrm{~m}^{2}$ (C) $56 \mathrm{~m}^{2}$ (D) $80 \mathrm{~m}^{2}$

1. Find the area of the square base.
2. Find the area of one triangular side.
3. Find the total area of the four triangular sides.
4. Calculate the total surface area.

The base is a square, and we know the side length is $4$ meters.
The area of a square is side multiplied by side.

So, the area of the base is $4 \cdot 4 = \textbf{16}$ square meters.
Write that down!

We know the base of each triangle is $4$ meters (same as the square).
We also know the slant height, which is like the triangle's height, is $5$ meters.
The area of a triangle is one-half base times height.

So, the area of one triangle is $\frac{1}{2} \cdot 4 \cdot 5 = \textbf{10}$ square meters.
Awesome!

Since there are four identical triangles, the total area of all the triangular sides is $4 \cdot 10 = \textbf{40}$ square meters.
We're almost there!

Now, we add the area of the square base (which was $\textbf{16}$ square meters) and the total area of the triangle sides (which was $\textbf{40}$ square meters).

So, the total surface area is $16 + 40 = \textbf{56}$ square meters.
Boom!

The total surface area of the pyramid is $56$ square meters, so the answer is (C).